Number Theory Books, 1996

• P-adic Numbers, p-adic Analysis and Zeta-Functions, (2nd edn.) N. Koblitz, Graduate Text 54, Springer 1996.
• Algorithmic Number Theory, Vol. 1, E. Bach and J. Shallit , MIT Press, August 1996
• Automorphic Forms and Representations, D. Bump, CUP 1996
• Notes on Fermat's Last Theorem, A.J. van der Poorten, Canadian Mathematical Society Series of Monographs and Advanced Texts, Wiley-Interscience, January, 1996, ISBN 0-471-06261-8
  • Review of Alf van der Poorten's Notes on Fermat's Last Theorem by Andrew Granville
• Additive Number Theory: The Classical Bases, Melvyn B. Nathanson, Graduate Texts in Mathematics 164, Springer 1996
• Additive Number Theory: Inverse Problems and the Geometry of Sumsets, Melvyn B. Nathanson, Graduate Texts in Mathematics 165, Springer 1996
• Arithmetic, Geometry and Coding Theory, Proceedings of a Conference at CIRM Luminy, June 28-July 2, 1993, Ed. R. Pellikaan, M. Perret, S.G. Vladut, de Gruyter 1996
• Duality in Analytic Number Theory, P.D.T.A. Elliot, Cambridge Tracts in Mathematics 122, CUP 1996
• Invitation to Arithmetic Geometry, Dino Lorenzini, Graduate Studies in Mathematics 9, AMS 1996
• Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, J.W.S. Cassels and E.V. Flynn, LMS Lecture Note Series 230, CUP 1996
• Sets of Multiples, R.R. Hall, Cambridge Tracts in Mathematics 118, CUP 1966
• Limit Theorems for the Riemann Zeta Function, A. Laurinčikas, Mathematics and its Applications 352, Kluwer 1996
• Handbook of Combinatorics, (eds.) R.L. Graham, M. Grötschel, L. Lovász, MIT Press 1996
• A Friendly Introduction to Number Theory, J.H. Silverman, Prentice Hall, Fall 1996
• Number Theory: an Introduction, D. Redmond, Pure and Applied Mathematics Series 201, Marcel Dekker 1996
• Area, Lattice Points, and Exponential Sums, M.N. Huxley, LMS Monograph 13, OUP 1996 (with errata)
• Orders of a Quartic Field, J. Nakagawa, Memoirs of the AMS 122/583, AMS 1996
• Multiplicative Galois Structure, A. Weiss, Fields Institute Monograph 5, AMS 1966
• Topics in Advanced Scientific Computation, R.E. Crandall, Springer 1996
• Analytic Number Theory: Proceedings of Conference in Honour of Heini Halberstam (ed) B.C. Berndt, H.G. Diamond, A.J. Hildebrandt, Progress in Mathematics 139, Birkhaüser 1996
• Basic Structures of Function Field Arithmetic, D. Goss, Springer, Ergebnisse der Math. Vol 35, due September 1996
  • Table of Contents (dvi 32K)
• The New Book of Prime Number Records, 3rd Edition, P. Ribenboim, Springer 1996, Review of first edition, S. S. Wagstaff Jr., Bull. Amer. Math. Soc. 21 (1989), 365-369
• Selected Papers of Yu I. Manin, Twentieth Century Mathematics Vol. 3, World Scientific 1996
• Perfect, Amicable and Sociable Numbers - A Computational Approach, Song Y. Yan, World Scientific 1996
• Mahler functions and transcendence, K. Nishioka, Springer Lecture Notes 1631, 1996
• New York Number Theory Seminar 1991-1995, (Ed) D.V. Chudnovsky, G.V. Chudnovsky, H. Cohn, M.B. Nathanson, Springer 1996
• Deformation of Galois Representations and Modular Forms, Lecture notes of Barry Mazur by Chuck Doran and Siman Wong, International Press, Harvard 1995
• The Mathematics of Paul Erdös, Volumes I and II, (ed.) R.L. Graham, J. Nesetril, Springer Algebra and Combinatorics 13 and 14, 1996 (no longer listed by Springer)
• An Arithmetic Riemann-Roch Theorem for Singular Arithmetic Surfaces, Wayne Aitken, Memoirs of the AMS, Vol 120/573, 1996
• Seminaire de Theorie des Nombres (15th: 1993, Paris), Ed. S. David, CUP 1996
• Theory of Algebraic Integers by Richard Dedekind, Translated by John Stillwell, CUP 1996
• Cohomology of Drinfeld Modular Varieties, Part II: The Arthur-Selberg Trace Formula, G. Laumon, Cambridge Studies in Advanced Mathematics 56, CUP 1996 (Appendix by J.L. Waldspurger)
• Proceedings of the Conference on Analytic and Elementary Number Theory (Vienna, July 1996) in honour of Edmund Hlawka's 80th birthday
• Chinese Remainder Theorem, C. Ding, D. Pei, A.Salomaa, World Scientific 1996
• Number Theory and Analysis, Ed. A.A. Karatsuba and V.I. Blagodatskikh, AMS 1996
• Multiplicative Galois Module Structure, Afred Weiss, Fields Institute Monographs 6 1996, Review, Cornelius Greither, Bull. Amer. Math. Soc. 34 (1997), 173-176
• Zahlentheorie, Armin Leutbecher, Springer, 1996

Number Theory Books, 1997

• Number Theory III, Serge Lang, Springer 1997
• Bilinear Algebra, An Introduction to the Algebraic Theory of Quadratic Forms , K. Szymiczek, Taylor and Francis 1997,
• Analytic Number Theory and Applications: Collection of papers on the occasion of the 60th birthday of Anatolli Alexeevich Karatsuba, Proc. Steklov Institute 218 (1997)
• Probabilistic Methods in the Theory of Numbers, J. Kubilius, 5th printing 1997, AMS
• The Hardy-Littlewood Method, R.C. Vaughan (2nd Edn) Cambridge Tract 125, CUP 1997
• Sequences, discrepancies and applications, R.F. Tichy, M. Drmota, Lecture Notes in Mathematic 1651, Springer 1997
• The semi-simple zeta function of quaternionic Shimura varieties, H. Reimann, Lecture Notes in Mathematic 1657, Springer 1997 (no longer listed by Springer)
• Algorithmische Zahlentheorie, Otto Forster, Vieweg 1996
• Spectral Theory of the Riemann Zeta-Function, Y. Motohashi, Cambridge Tract 127, CUP 1997
• Realizations of Polylogarithms, J. Wildeshaus, Springer, Lecture Notes in Mathematics Vol 1650 (no longer listed by Springer)
• Number Theory IV: Transcendental Numbers, Yu.V. Nesterenko, N.I. Feldman, Springer, Encyclopaedia of Mathematical Sciences Vol 44
• Number Theory with Computer Applications, R. Kumanduri and C. Romero, Prentice Hall 1997
• Fundamental number theory with applications, Richard Mollin, CRC Press 1997
• The Book of Numbers, J.H. Conway, R.K. Guy, Springer 1996
• Les Nombres Premiers, G. Tenenbaum, M. Mendes France, Que Sais-je? N° 571, PUF 1997, ISBN 2-13-048399-2
• Zahlentheorie, Algebraische Zahlen und Funktionen, H. Koch, Aufbaukurs Mathematik, Vieweg Studium, 1997, ISBN 3-528-07272-5
• The Proceedings of the Organic Mathematics Workshop, J. Borwein, P. Borwein, R. Corless, L. Jorgenson, Canadian Math. Soc. Conference Proceedings No 20, 1997
• Pi: A Source Book, L. Berggren, J. Borwein, P. Borwein, Springer-Verlag 1997
• Number Theory, Ed. V.K. Murty, M. Waldschmidt, Contemporary Mathematics, 210 AMS 1997
• Topics in Classical Automorphic Forms, H. Iwaniec, Graduate Studies 17, AMS 1997
• Euler Products and Eisenstein Series, G. Shimura, CBMS Regional Conference Series 93, AMS 1997
• Exercicés Corrigis de Théorie Analytique et Probabiliste des Nombres, G. Tenenbaum, Cours Spécialisés - Collection SMF 1997
• Elliptic Curves, Function Theory, Geometry, Arithmetic, H. McKean, V. Moll, CUP 1997
• Diophantine Approximation and Abelian Varieties, B. Edixhoven, J.-H. Evertse, Springer Lecture Notes 1566 (second printing 1997)
• An Introduction to the Geometry of Numbers, J.W.S. Cassels, Classics in Mathematics, Springer 1997
• The Queen of Mathematics, A Historical Guide to Number Theory, Jay Goldman, CRC Press
• Modular Forms and Fermat's Last Theorem, G. Cornell, J.H. Silverman, G. Stevens (Editors), Springer 1997
• Automorphic Forms on SL2(R), A. Borel, Cambridge Tract 130, CUP 1997
• Non-vanishing of L-Functions and Applications, M.R. Murty, V.K. Murty, Progress in Mathematics 157, Birkhaüser 1997
• Analytic Number Theory, D.J. Newman, Graduate Text 177, Springer 1997
• The Sensual (Quadratic) Form, J.H. Conway, Carus Mathematical Monograph 26, 1997 MAA
• Analytic Number Theory, Edited by Y. Motohashi, LMS Lecture Note Series, 1997
• Sieve Methods, Exponential Sums and their Applications in Number Theory, Edited by G.R.H. Greaves, G. Harman, M.N. Huxley, LMS Lecture Note Series, 1997
• Analytic and Probabilistic Methods in Number Theory, Volume 4, New Trends in Probability and Statistics, Edited by A. Laurinčikas, E. Manstavicius and V. Stakenas, VSP Science 1997
• Lectures on the Mordell-Weil theorem, J.-P. Serre, Aspects of Mathematics 15, Vieweg 1997

Number Theory Books, 1998

• A Tribute to Mathematical Legend Paul Erdös, K. Alladi, P.D.T.A. Elliot, A. Granville, G. Tenenbaum, Vol 1, Developments in Mathematics, Kluwer 1998
• SL2(R), Serge Lang, Graduate Text 105, Springer 1998
• Elliptische Funktionen und Modulformen, Max Koecher, Aloys Krieg, Springer Lehrbuch, 1998
• The Theory of Partitions, G.E. Andrews, Encyclopaedia of Mathematics and Its Applications 2, Addison-Wesley 1976, reissued CUP 1998
• Lattice Basis Reduction Algorithms and their Applications, Gudrun Susanne Wetzel, Shaker Verlag 23, 1998
• Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A. O. L. Atkin, Ed. D. A. Buell, J. T. Teitelbaum, AMS/IP Studies in Advanced Mathematics, Vol 7, 1998
• Elementary Number Theory, G.A.J. Jones, J.M. Tyrer-Jones, Undergraduate Texts in Mathematics, Springer 1998
• Cubic Metaplectic Forms and Theta Functions, N. Proskurin, Lecture Notes in Mathematics 1677, Springer 1998 (no longer listed by Springer)
• Abelian Varieties with Complex Multiplication and Modular Functions, G. Shimura, Princeton Mathematical Series 46, 1998
• The Dynamical System Generated by the 3n+1 Function, G.J. Wirsching, Lecture Notes in Mathematics 1681, Springer 1998
• On the Search of Genuine p-adic Modular L-Functions for GL(n), H. Hida, Memoires de la Société Mathématique de France, 1998
• Édouard Lucas and Primality Testing, Hugh C. Williams, Wiley, Canadian Mathematical Society Series of Monographs and Advanced Texts, 1998
• Gauss and Jacobi Sums, B.C. Berndt, R.J. Evans, K.S. Williams, Wiley, Canadian Mathematical Society Series of Monographs and Advanced Texts, 1998
• The Algorithmic Resolution of Diophantine Equations, A Computational Cookbook, N.P. Smart, LMS Lecture Notes, CUP 1998
• Ideal Systems, An Introduction to Multiplicative Ideal Theory, Franz Halter-Koch, Vol 211, Pure and Applied Mathematics, Marcel Dekker 1998
• Metric Number Theory, G. Harman, OUP 1998
• Stream Ciphers and Number Theory, T.W. Cusick, C. Ding, A. Renvall, Akademika, Norway
• Number Theory with Applications, James A. Anderson, James M. Bell, Prentice Hall, 1997
• Rational Points, G. Faltings, G. Wüstholz, Aspects of Mathematics 6, 1998, Vieweg
• Number Theory: A Programmer's Guide, Mark A. Herkommer, McGraw-Hill, 1998
• The Theory of Algebraic Number Fields, A translation of Hilbert's Zahlbericht by I.T. Adamson
• Number Theory and Its Applications, Ed. Y.C. Yıldırın, S.A. Stepanov, Marcel Dekker 1998
• The man who loved only numbers, by Paul Hoffman, Fourth Estate, London 1998 (reviewed by Paul Halmos)
• Algebraic Aspects of Cryptography , N. Koblitz, Springer 1998
• Combinatorial Algorithms: Generation, Enumeration, and Search, D. Kreher, D.R. Stinson, CRC Press 1998
• Kryptographie in C und C++, M. Welschenbach, Springer 1998, 2nd edition 2005 in English
• Hua Loo-Keng, a Biography, Wang Yuan, Springer 1998 (no longer listed by Springer)
• Modern Computer Algebra, J. von zur Gathen, J. Gerhard, CUP 1998
• Diophantus and Diophantine Equations, I.G. Bashmakova, CUP, 1998
• Galois Representations in Arithmetic Algebraic Geometry, Ed. A.J. Scholl, R.L. Taylor, LMS Lecture Notes 254, CUP 1998
• Handbook of Applied Cryptography, A.J. Menezes, P.C. van Oorschot, S.A. Vanstone , CRC Press 1998
• Galois Representations in Arithmetic Algebraic Geometry, A.J. Scholl, R.L. Taylor, LMS Lecture Notes Series 254, CUP 1998
• Algebraic Geometry, D. Bump, World Scientific 1998
• Groups acting on hyperbolic space: harmonic analysis and number theory, J. Elstrodt, F. Grunewald, J. Mennicke, Springer 1998
• Ramanujan's Notebooks Part V, B.C. Berndt, Springer 1998
• Ramanujan's Notebooks Part II, B.C. Berndt, Springer 1998

Number Theory Books, 1999

• Theory of Linear and Integer Programming, A. Schrijver, Wiley 1999
• Fourier Analysis on Number Fields, D. Ramakrishnan, R.J. Valenza, Graduate Text 186, Springer 1999
• Fermat's Last Theorem for Amateurs, P. Ribenboim, Springer 1999
• Problems in Algebraic Number Theory, J. Esmonde, M.R. Murty, Graduate Text 190, Springer 1999
• Number Theory for Computing, Song Y. Yan, Springer May 1999
• Elementary Number Theory in Nine Chapters, J.J. Tattersall, CUP, July 1999
• Algorithmic Algebra and Number Theory, (Selected papers From a Conference Held at the University of Heidelberg in October 1997), Ed. B.H. Matzat, G-M. Greuel, Springer 1999 (no longer listed at Springer)
• Proceedings of the Fifth Conference of the Canadian Number Theory Association, Ed. R. Gupta, K.S. Williams, AMS 1999
• Number theoretic methods in cryptography: Complexity lower bounds, I. Shparlinski, PCS 17, Birkhäuser, 1999
• The Theory of Classical Valuations, P. Ribenboim, Springer 1999
• Elliptic Curves and Cryptography, I. Blake, G. Seroussi, N. Smart, CUP, June 1999
• Topics In Number Theory, Proceedings of a conference in honor of B. Gordon and S. Chowla, Ed. S. Ahlgren, G. Andrews and K. Ono, Kluwer 1999
• Finite fields: Theory and computation, I. Shparlinski, Kluwer Academic Publishers 1999
• Algebraic Number Theory, R.A. Mollin, CRC Press 1999
• Progress in Number Theory, Ed. K. Györy, H. Iwaniec, J. Urbanowicz, De Gruyter 1999
• Prime Numbers and their distribution, G. Tenenbaum, M. Mendès France, AMS 1999
• Sphere Packing, Lattices and Groups, (Third Edition), N. Sloane, J.H. Conway, Springer 1999
• Emerging Applications of Number Theory, (Ed.) D.A. Hejhal, J. Friedman, M.C. Gutzwiller, A.M. Odlyzko, Springer 1999
• Introdução à Teoria dos Números, José Plinio de Oliveira Santos, IMPA 1999
• Voronoi's Impact on Modern Science, Proceedings of the Voronoi Conference at Kiev, 1998
• Analytic and Elementary Number Theory, (A Tribute to Mathematical Legend Paul Erdös), Developments in Mathematics 1, Springer
• Algebraic Number Theory, J. Neukirch, Springer 1999
• Character Sums with Exponential Functions and their Applications, S. Konyagin, I. Shparlinski, CUP 1999
  • Review of Character sums with Exponential Functions and their Applications, S. Konyagin, I. Shparlinski (Reviewer: W. Duke)
• Automorphic Forms, Automorphic Representations, and Arithmetic, Ed. R.S. Doran, Z-L. Dou, G.T. Gilbert, Proc. Symposia in Pure Mathematics 66, 1999, AMS
• Elliptic curves and their applications to cryptography, A. Enge, Kluwer 1999
• Fourier analysis on finite abelian groups and applications, A. Terras, LMS Student Texts, CUP 1999
• Structure Theory of Set Addition, Jean-Marc Deshouillers, Bernard Landreau, Alexander A. Yudin (Ed.) Astérisque 258 (1999)
• Arithmetic theory of elliptic curves, J. Coates, R. Greenberg, K. Ribet, K. Rubin, C. Viola (Ed), Springer Lecture Notes 1716, 1999
• Number Theory 1, Fermat's Dream, Translation of Mathematical Monographs, Vol. 186, AMS 2000
• Metric Diophantine Approximation on Manifolds, V.I. Bernik, M.M. Dodson, CUP 1999
• Solved and Unsolved Problems in Number Theory, Daniel Shanks, Third Edition, (American Mathematical Society Bookstore)
• Getaltheorie voor beginners, F. Beukers, Epsilon Uitgaven, Utrecht 1999
• Algebra and Number Theory, Ed. M. Boulagouaz, J.-P. Tignol, Lecture Notes in Pure and Applied Mathematics 208, Marcel Dekker 1999
• Integral Quadratic Forms and Lattices, M-H. Kim, J.S. Hsia, Y. Kitaoka, Contemporary Mathematics 249, AMS 1999
• Fundamental Problems in Algorithmic Algebra, C.K. Yap, OUP 1999
• Random Matrices, Frobenius Eigenvalues and Monodromy, N.M. Katz, P. Sarnak, AMS Colloquium Publications Vol 45 1999
• Oxford Figures, J. Fauvel, R. Flood, R.J. Wilson, OUP 1999
• Number Theory and Its Applications, Ed. S. Kanemitsu, K. Györy, Developments in Mathematics 2, Kluwer 1999
• Codes on Algebraic Curves, S.A. Stepanov, Kluwer 1999
• Classical Theory of Algebraic Numbers, P. Ribenboim, Universitext, Springer 1999
• Regulators in Analysis, Geometry, and Number Theory, Ed. A. Reznikov, N. Schappacher, Birkhäuser 1999
• Elementary Number Theory, Edmund Landau , AMS Chelsea Publishing 1999

Number Theory Books, 2000

• Collected papers IV (1990-1996), Serge Lang, Springer 2000
• Primes, a computational perspective, C. Pomerance, R. Crandall, Springer 2000
• Polynomials with special regard to reducibility, Andrzej Schinzel, CUP 2000
• The Collected Papers of Sarvadaman Chowla, (Vols 1-3), Centre de Recherches Mathématiques , Université de Montréal, 2000
• Advanced topics in computational number theory, H. Cohen, Graduate Text 193, Springer, January 2000
• Elementary Methods in Number Theory, M.B. Nathanson, Graduate Text in Mathematics 195, Springer 2000
• The Fourier-Analytic Proof of Quadratic Reciprocity, M.C. Berg, Wiley 2000
• Diophantine Approximation on Linear Algebraic Groups, M. Waldschmidt, Grundlehren Series 326, Springer 2000
• The Development of Prime Number Theory, W. Narkiewicz, Monographs in Mathematics XII, Springer 2000
• Reciprocity Laws - From Euler to Eisenstein, F. Lemmermeyer, Monographs in Mathematics XIX, Springer 2000
• Diophantine Geometry, An Introduction, M. Hindry, J.H. Silverman, Graduate Text 201, Springer 2000
• A Course in p-adic Analysis, A. Robert, Graduate Text 198, Springer 2000
• Cohomology of Number Fields, J. Neukirch, A. Schmidt, K. Wingberg, Grundlehren Series 323, Springer 2000; plus errata
• My Numbers, My Friends , P. Ribenboim, Monographs in Mathematics, Springer 2000
• An Introduction to Cryptography, R.A. Mollin, Chapman and Hall/CRC, Boca Raton, London, New York, Washington D.C. 2000
• Codes and Curves, J. Walker, Student Mathematical Library 7, 2000, AMS
• An Introduction to the Theory of Local Zeta Functions, J-I. Igusa, AMS/IP Studies in Advanced Mathematics 14, 2000, AMS
• Number Theory, Ed. R.P. Bambah, V.C. Dumir, R.J.H. Gill, Trends in Mathematics, Birkhäser 2000 (not listed)
• Number Theory: Algebraic Numbers and Functions, H. Koch, AMS Graduate Studies in Mathematics, Vol 24, 2000
• Arithmeticity in the Theory of Automorphic Forms, G. Shimura, AMS Mathematical Surveys and Monographs 82, 2000
• Exploring the Number Jungle: A Journey into Diophantine Analysis, E.B. Burger, AMS Student Mathematical Library 8, 2000
• Fractal Geometry and Number Theory, M.L. Lapidus, M. van Frankenhuysen. Birkhaüser, 2000
• Selected Works of Ilya Piatetski-Shapiro, Ed. J. Cogdell, S. Gindikin, P. Sarnak. AMS Collected Works 15, 2000
• Euler Systems, K. Rubin, Annals of Mathematics Studies, Princeton University Press 2000
• Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, L.N. Childs, AMS Mathematical Surveys and Monographs, 80 (2000)
• Algebraic Number Theory and Diophantine Analysis, Proceedings of the International Conference, held in Graz, Austria, August 30-September 5, 1998 Editors: Franz Halter-Koch, Robert F. Tichy
• Galois Cohomology of Elliptic Curves, J. Coates, R. Sujatha, Tata Institute of Fundamental Research Series, AMS 2000
• Modular Forms and Galois Cohomology, H. Hida, Cambridge Studies in Advanced Mathematics, CUP 2000
• Algorithmic Number Theory, Proceedings of ANTS-IV, LNCS 1838, Springer 2000
• An Introduction to Cryptography, R.A. Mollin, Chapman and Hall/CRC Press, 2000
• The Fermat Diary, C.J. Mozzochi, AMS 2000
• A Course in Computational Number Theory, D. Bressoud, S. Wagon, Springer 2000
• Introduction to Cryptography, J. Buchmann, Undergraduate Text Springer 2000
• Invitation to higher local fields, (editors) Ivan Fesenko and Masato Kurihara, Geometry and Topology Monographs, Volume 3, 2000
• Congruences for L-Functions, J. Urbanowicz, K.S. Williams, Mathematics and its Applications, 511, Kluwer 2000
• Quantization and Non-holomorphic Modular Forms, A. Unterberger, Lecture Notes in Mathematics 1742, Springer 2000
• Meromorphic Functions over non-Archimedean Fields, Pei-Chu Hu, Chung-Chun Yang, Mathematics and its applications 522, Kluwer 2000
• Mathematics Unlimited - 2001 and Beyond, B. Engquist, W. Schmid, (Ed), Springer 2000 (contains articles by Darmon, Faltings, Koblitz, van der Geer)
• Multidimensional continued fractions, F. Schweiger, OUP 2000
• Geometry of numbers, C.D. Olds, A. Lax, G. Davidoff, New Library Series 41, MAA 2000 (Review by Henry Cohn)

Number Theory Books, 2001

• Réseaux euclidiens, designs sphériques et formes modulaires, Jacques Martinet, Monographie 37 de l'Enseignement Mathématique, Genève
• Números Primos: mistérios e recordes, Paulo Ribenboim, IMPA, 2001
• Nevanlinna's Theory of Value Distribution, W. Cherry, Z. Ye, Monographs in Mathematics, Springer 2001
• A brief guide to algebraic number theory, Peter Swinnerton-Dyer, LMS Student Text, CUP 2001
• Problems in Analytic Number Theory, M.R. Murty, Graduate Text in Mathematics 206, 2nd edition, Springer 2008
• Sieves in Number Theory, G. Greaves, Ergebnisse der Mathematik 43, Springer 2001
  • Sieves in number theory, by George Greaves, Reviewer H. Halberstam, Bull. AMS. 40, 2003, 109-119
• Introduction to Algebraic Independence Theory, Y.V. Nesterenko, P. Philippon (Eds.) Lecture Notes in Mathematics 1752, Springer 2001
• Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform, R. Kiehl, R. Weissauer, Ergebnisse der Math. 42, Springer 2001
• The Discrepancy Method , B. Chazelle, CUP 2001
• Number theory arising from finite fields, J. Knopfmacher, Wen-Bin Zhang, Marcel Dekker 2001
• Number Theory, Proceedings of the Turku Symposium in memory of Kustaa Inkeri, (Ed. M. Jutila, T. Metsänkylä), de Gruyter 2001
• Arithmetic Algebraic Geometry, B. Conrad, K. Rubin (Editors), IAS/Park City Mathematics Series 9, AMS 2001
• Theta Constants, Riemann Surfaces and the Modular Group: An Introduction with Applications, H.M. Farkas, I. Kra, Graduate Studies in Mathematics, AMS 2001
• Nevanlinna Theory and its Relation to Diophantine Approximation, Min Ru, World Scientific, 2001
• Torsors and Rational Points, A. Skorobogatov, Cambridge Tract 144, CUP
• Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform, R. Kiehl, R. Weissauer, Ergebnisse der Mathematik 42, Springer 2001
• Class Field Theory - Its Centenary and Prospect, Ed. Katsuya Miyake, Advanced Studies in Pure Mathematics 30, 2001
• The Decomposition of Primes in Torsion Point Fields, C. Adelmann, Lecture Notes in Mathematics 1761, Springer 2001
• Invitation to the Mathematics of Fermat-Wiles, Y. Hellegouarch, Academic Press 2001
• Ramanujan: Essays and Surveys, (Ed.) B.C. Berndt, R.A. Rankin, History of Mathematics Series, November 2001, AMS
• Rational Points on Curves over Finite Fields, H. Niederreiter, C. Xing, Lecture Note Series 285, CUP 2001
• Pseudo-Differential Equations and Stochastics over Non-Archimedean Fields, A.N. Kochubei, Marcel Dekker 2001
• Local Fields and Their Extensions, (Second Edition) I.B. Fesenko, S.V. Vostokov, 2001
• Number Theory in Function Fields, M. Rosen, Graduate Text 210, Springer 2001
• Kenkichi Iwasawa Collected Papers, Ed. G. Fujisaki, K. Kazuya, M. Kuhira, S. Nakajima, volumes 1-2, Springer 2001
• Public-Key Cryptography and Computational Number Theory, Ed. K. Alster, J. Urbanowicz, H.C. Williams, de Gruyter 2001
• The Geometry and Cohomology of Some Simple Shimura Varieties, M. Harris, R. Taylor, Annals of Mathematics Studies 151, Princeton University Press, 2001
• Twisted L-Functions and Monodromy, N.M. Katz, Annals of Mathematics Studies 150, Princeton University Press, 2001
• q-Series with Applications to Combinatorics, Number Theory, and Physics, Ed. Bruce Berndt, Ken Ono, Contemporary Mathematics 291 2001
• Theorie d'Iwasawa des Representations p-Adiques Semi-Stables, B. Perrin-Riou, Mémoires de la Société Mathématique de France 84, AMS 2001
• The Decomposition of Primes in Torsion Point Fields, C. Adelmann, Lecture Notes in Mathematics 1761, 2001

Number Theory Books, 2002

• Number Theory for the Millennium I, II, III, Ed. Bruce Berndt et al., A.K. Peters 2002
• Cryptanalysis of Number Theoretic Ciphers, Samuel S. Wagstaff Jr., Mikhail J. Atallah, Chapman and Hall/CRC, 2002
• Number Theory, H. Hasse (reprint), Springer 2002
• 17 Lectures on Fermat Numbers, M. Krizek, F. Luca, L. Somer, CMS books in mathematics 9, Springer 2002
• Lectures on Hilbert Modular Varieties and Modular Forms, E.Z. Goren, AMS, 2002
• Rational Points on Algebraic Varieties, E. Peyre, Y. Tschinkel, Progress in Mathematics 199, Birkhäuser 2002
• The Prime Number Theorem, G.J.O. Jameson, LMS Student Text, to appear 2002
• Computational Excursions in Analysis and Number Theory, P. Borwein, CMS Books in Mathematics 11, Springer NY
• The Lifted Root Number Conjecture and Iwasawa Theory, J. Ritter, A. Weiss, Memoirs of the AMS 157, AMS 2002
• Cohomology of Arithmetic Groups, L-Functions and Automorphic Forms, T. N. Venkataramana, AMS/Tata Institute of Fundamental Research Series, 2002 History of the Theory of Numbers, Leonard Eugene Dickson, AMS Chelsea Publishing 2002
• Diophantine equations and power integral bases, István Gaál, Birkhaüser, 2002
• Algebraic geometry and arithmetic curves, Qing Liu, Oxford Graduate Texts in Mathematics, OUP 2002
• Collected Papers of Wayne L. McDaniel, Ed. Paulo Ribenboim, Volume 122, Queen's Papers in Pure and Applied Mathematics
• Introduction to p-adic Analytic Number Theory, M. Ram Murty, AMS/IP Studies in Advanced Mathematics 27, AMS 2002
• A Panorama of Number Theory or the View from Baker's Garden, Ed. G. Wüstholz, CUP 2002
• Analytic Number Theory, Ed. Chaohua Jia, Kohji Matsumoto, Kluwer 2002
• Galois Theory of p-Extensions, H. Koch, Springer Monographs in Mathematics 2002
• RSA and Public-Key Cryptography, R.A. Mollin, CRC Press 2002
• Grothendieck Duality, B. Conrad, Lecture Notes in Mathematics 1750, 2002
• The Goldbach Conjecture, Ed. Yuan Wang, World Scientific 2002
• Algebraic Number Theory and Algebraic Geometry, Papers dedicated to A.N. Parshin on the occasion of his 60th birthday, Ed. S. Vostokov, Y. Zahrin, Contemporary Mathematics 300, AMS 2002
• Algebraic Curves and one-dimensional fields, F. Bogomolov, T. Petrov, Courant Lecture Notes 8, AMS 2002
• Number theoretic methods, Ed. Shigeru Kanemitsu, Chaohua Jia, Developments in Mathematics, Kluwer 2002
• Chabauty methods and covering techniques applied to generalized Fermat equations, CWI Tract 133, Nils Bruin 2002
• The Honors Class: Hilbert's Problems and their Solvers, Ben Yandell. A.K. Peters 2002
• Ergodic theory of numbers, Karma Dajani, Cor Kraaikamp, MAA Carus Monograph 29, 2002

Number Theory Books, 2003

• Perfect Lattices in Euclidean Spaces, J. Martinet, Grundlehren der mathematischen Wissenschaften 327, Springer 2003
  • Review of J.Martinet's Perfect lattices in Euclidean spaces, by Gabriele Nebe
• Recurrence sequences, G. Everest, A.J. van der Poorten, I. Shparlinski, T. Ward, AMS Surveys and Monographs, volume 104, 2003
• Class Field Theory: From Theory to Practice, Georges Gras, corr. 2nd ed., Springer Monographs in Mathematics, Springer 2005, xiii+507 pages
• Paul Erdös and His Mathematics, G. Halász, L. Lovász, M. Simonvits, V.T. Sós, Bolyai Mathematical Studies 11, 2003
• Topics in the Theory of Numbers , J. Suranyi, P. Erdös, B. Guiduli, Undergraduate Texts in Mathematics, Springer 2003
• Algebraic Functions and Projective Curves, D. Goldschmidt, Graduate Text in Mathematics 215, Springer 2003
• Elements of Number Theory, J. Stillwell, Undergraduate Texts in Mathematics, Springer 2003
• Pell's Equation, E. Barbeau, Problem Books in Mathematics, Springer 2003
• A Primer of Analytic Number Theory, Jeffrey Stopple, CUP 2003
• Elliptic Curves: A computational approach, Susanne Schmitt, Horst Zimmer, Studies in Mathematics 31, De Gruyter 2003
• Homepage for Prime Obsession (John Derbyshire)
  • Sid Graham's Review of Prime Obsession by John Derbyshire
• Music of the primes, Marcus du Sautoy, 2003
  • Stacy Langton's Review of Music of the primes, by Marcus du Sautoy
• The Riemann Hypothesis, Karl Sabbagh, Farrah, Strauss and Giroux, 2003
  • Sid Graham's Review of The Riemann Hypothesis by Karl Sabbagh
• Automatic Sequences: Theory, Applications, Generalizations, J.-P. Allouche, J. Shallit, CUP 2003
• Elliptic Curves, Modular Forms and Cryptography, A.K. Bhandari, D.S. Nagaraj, B. Ramakrishnan, T.N. Venkataramana, Hindustan Book Agency, 2003
• Diophantine Approximation, Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 - July 6, 2000 Springer 2003
• Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms, M. Courtieu, A.A. Panchishkin, Lecture Notes in Mathematics 1471, Springer 2003
• An Introduction to the Langlands Program, Ed. Joseph Bernstein, Stephen Gelbart, Birkhaüser 2003
• A Collection of Manuscripts Written in Honour of Kazuya Kato on the Occasion of His Fiftieth Birthday, Ed. S. Bloch, I. Fesenko, L. Illusie, M. Kurihara, S. Saito, T. Saito, P. Schneider, Documenta Mathematica, 2003
• Elliptic Curves: Number Theory and Cryptography, Lawrence C. Washington, Chapman Hall/CRC 2003
• Arithmetic of higher-dimensional algebraic varieties, Yuri Tschinkel, Bjorn Poonen, Progress in Mathematics 226, Birkhäuser 2003
• Mathematical Constants, Steve Finch, CUP 2003
• Galois theory and modular forms, Ed. Ki-ichiro Hashimoto, Katsuya Miyake, Hiroaki Nakamura, Developments in Mathematics 11, Kluwer 2003
• Many Rational Points: Coding Theory and Algebraic Geometry , Norman Hurt, Mathematics and its Applications 564, Kluwer 2003
• The Collected Papers of Wilhelm Ljunggren, Ed. Paulo Ribenboim, Queen's papers in pure and applied mathematics 115 2003
• Dan Segal's review of Gamma, by Julian Havil, Princeton University Press 2003
• The Lerch zeta-function, A. Laurinčikas, R. Garunkstis, Springer 2003
• Kloosterman sums and Maass forms, Volume 1, Roger C. Baker, Kendrick Press 2003
• Equations over finite fields: an elementary approach, Second Edition, Wolfgang M. Schmidt, Kendrick Press 2003 (also see review in MathSciNet)

Number Theory Books, 2004

• Number Theory and Algebraic Geometry, Ed. Miles Reid, Alexei Skorobogatov, LMS Lecture Notes 303, 2004
• Algoritmos deterministas de primalidad, Pedro Berrizbeitia, 2004
• Forms of Fermat equations and their zeta functions, Lars Brünjes, World Scientific 2004
• Introductory Algebraic Number Theory, Şaban Alaca, Kenneth Williams, CUP 2004
  • Errata (pdf file)
  • Selected solutions
• Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups, Goro Shimura, Mathematical Surveys and Monographs, 109, AMS 2004
• Kolyvagin Systems, B. Mazur, K. Rubin, Memoirs of the American Mathematical Society, 168, AMS 2004
• The Number $\pi$, Pierre Eymard and Jean-Pierre Lafon, AMS 2004
• Rational Points on Modular Elliptic Curves, Henri Darmon, CBMS Regional Conference Series in Mathematics 101, AMS 2004
• Elliptic Curves, D. Husemöller, Graduate Texts in Mathematics 111, Springer 2004
• The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series, Ken Ono, CBMS Monograph 102, AMS, January 2004
• Number Theory from an analytic point of view (Théorie de Nombre d'un point de vue analytique), Badih Ghusayni
• Unusual Applications of Number Theory, M. Nathanson, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 64, AMS May 2004
• An Introduction to the Theory of Numbers, Leo Moser, The Trillia Group 2004
• The Fermat Proof, C. J. Mozzochi, The Allahabad Mathematical Society
• Analytic Number Theory, Henryk Iwaniec, Emmanuel Kowalski, Colloquium Publications 53, AMS 2004
  • Review by Alexandru Zaharescu of Analytic number theory by Henryk Iwaniec and Emmanuel Kowalski
• High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Alf van der Poorten, Andreas Stein (editors), Fields Institute Communications, 41 AMS 2004
• Nagell's collected works (4 volumes)
• Elliptic Curves, Dale Husemöller, Graduate Text 111, Springer 2004
• Quaternion Orders, Quadratic Forms, and Shimura Curves, Montserrat Alsina, Pilar Bayer, CRM Monograph Series, 22, 2004
• Number Theory, Ed. Hershy Kisilevsky, Eyal Goren, CRM Proceedings & Lecture Notes, 36, July 2004, AMS
• Function field arithmetic, Dinesh Thakur, World Scientific 2004
• p-Adic Automorphic Forms on Shimura Varieties, H. Hida, Springer Monographs in Mathematics, 2004
• Absolute CM-Periods, Hiroyuki Yoshida, OUP 2004
• Approximation by Algebraic Numbers, Yann Bugeaud, Cambridge Tract 160, CUP October 2004
  • Review of Yann Bugeaud's book Distribution modulo one and Diophantine approximation, by Jean-Paul Allouche
• Heegner Points and Rankin L-Series, Edited by Henri Darmon, Shou-wu Zhang, CUP October 2004
• Handbook of Number Theory II, Jozsef Sándor, Borislav Crstici, August 2004, Springer
• Heegner Modules and Elliptic Curves, Martin L. Brown, Lecture Notes in Mathematics, 1849, Springer 2004
• Stark's Conjectures: Recent Work and New Directions, Ed. David Burns, Christian Popescu, Jonathan Sands, David Solomon, Contemporary Mathematics 358, AMS 2004
• Analytic Number Theory, An Introductory Course, Paul Bateman & Harold Diamond, World Scientific, September 2004
• Elementary and Analytic Theory of Algebraic Numbers, (Third Edition), W. Narkiewicz, Springer 2004
• Unsolved Problems in Number Theory, Richard Guy, 3rd edition, Springer 2004
• Galois Theory, David Cox, John Wiley & Sons, 2004
• Heegner Modules and Elliptic Curves, Martin Brown, Lecture Notes in Mathematics, Vol. 1849, Springer 2004
• A Field Guide to Algebra, Antoine Chambert-Loir, Undergraduate Text in Mathematics, Springer, November 2004
• Integer Partitions, George Andrews, Kimmo Eriksson, CUP, December 2004
• Making Transcendence Transparent: An intuitive approach to classical transcendental number theory, Ed Burger, Robert Tubbs, Springer 2004
• Geometric Aspects of Dwork Theory, Ed. Alan Adolphson, Francesco Baldassarri, Pierre Berthelot, Nicholas Katz, Francois Loeser, Volumes I, II, de Gruyter 2004
• Trigonometric Sums in Number Theory and Analysis, Gennady I. Arkhipov, Vladimir N. Chubarikov, Anatoly A. Karatsuba, Expositions in Mathematics 39, De Gruyter 2004
• Un cours de théorie analytique des nombres, Emmanuel Kowalski, Cours Spécialisés-Collection SMF 13, 2004
• Handbook of Number theory II, J. Sándor, B. Crstici, Kluwer 2004
• Algorithmic Number Theory, Proceedings of ANTS-VI, Ed. Duncan Buell, Springer 2004
• Guide to Elliptic Curve Cryptography, D. Hankerson, A. Menezes, S. Vanstone, Springer 2004
• Introduzione alla Crittografia, Alessandro Languasco and Alessandro Zaccagnini, Ulrico Hoepli Editore, Milano, 2004
• Mathematical Journeys, Pete Schumer, Wiley 2004
• Forms of Fermat Equations and Their Zeta Functions, Lars Brünjes, World Scientific 2004

Number Theory Books, 2005

• Arithmetic Differential Equations, Alexandru Buium, AMS Mathematical Surveys and Monographs 118 2005
• Distribution of Sequences: A Sampler, Oto Strauch, Stefan Porubský, Peter Lang Publishing Group 2005
• Modular Curves and Abelian Varieties, Ed. John Cremona, Joan-Carles Lario, Jordi Quer, Ken Ribet, Birkhäuser 2005
• A First Course in Modular Forms, Fred Diamond, Jerry Shurman, Graduate Text 228, Springer January 2005, Errata, Review by Frank Calegari, Bull. AMS. 43 (2006), 415-421
• Introduction à la théorie des nombres, G.H. Hardy, E.M. Wright, OUP 2008
• Field Arithmetic, Michael Fried, Moshe Jarden, revised edition, Ergebnisse Volume 11, Springer 2005
• A Computational Introduction to Number Theory and Algebra, 2nd edition, Victor Shoup, CUP 2008
• An Introduction to Number Theory, G. Everest, T. Ward, Graduate Text 232, Springer 2005
• Advanced Analytic Number Theory: L-Functions, Carlos Moreno, Mathematical Surveys and Monographs 115, 2005
• Analytic Methods for Diophantine Equations and Diophantine Inequalities, H. Davenport (Ed. Tim Browning), CUP 2005
• Diophantine analysis, Jörn Steuding, CRC Press/ Chapman & Hall, Boca Raton, 2005
• The St. Petersburg School of Number Theory, B.N. Delone, translated by R.G. Burns, History of Mathematics 26, AMS September 2005
• Arithmetic Differential Equations, Alexandru Buium, Mathematical Surveys and Monographs 118, AMS September 2005
• Arithmetic Noncommutative Geometry, Matilde Marcolli, University Lecture Series 36, AMS July 2005
• Handbook of Elliptic and Hyperelliptic Curve Cryptography, H. Cohen, G. Frey, R.M. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren, CRC Press, July 2005
• On Sums of Sixteen Biquadrates, J. Deshouillers, K. Kawada, T.D. Wooley, Mémoire de la Société Mathématique de France, 100, 2005
• Automorphic forms (I), Proceedings of the Semester of the Émile Borel Center, Spring 2000, Ed: Jacques Tilouine, Henri Carayol, Michael Harris and Marie-France Vignéras, Asterisque 298, 2005
• Selected papers of Wang Yuan, (Ed.) Wang Yuan, World Scientific 2005
• Ramanujan's Lost Notebook Part I, George Andrews, Bruce Berndt, Springer 2005
• Geometric Methods in Algebra and Number Theory, Fedor Bogomolov, Yuri Tschinkel (Eds.) Progress in Mathematics, 235, Birkhäuser 2005
• Zeta Functions, Topology and Quantum Physics, (Eds.) T. Aoki, S. Kanemitsu, M. Nakahara, Y. Ohno, Developments in Mathematics, 14, Springer 2005
• Posn(R) and Eisenstein Series, Serge Lang, Jay Jorgenson, Lecture Notes in Mathematics 1868, Springer 2005
• The Diophantine Frobenius Problem, Jorge Luis Ramírez Alfonsín, OUP, 2005
• Number Fields and Function Fields - Two Parallel Worlds, Ed. Gerard van der Geer, Ben Moonen, René Schoof, Progress in Mathematics, 239, Birkhäuser 2005
• An Introduction to Sieve Methods and Their Applications, Alina Cojocaru, Ram Murty, LMS Student Texts 66, December 2005
• Continued fractions, Doug Hensley, World Scientific, 2005
• Automorphic Representations, L-Functions and Applications: Progress and Prospects, Ed. James Cogdell etc. de Gruyter 2005
• Introduction to Modern Number Theory, (2nd edition of Number Theory I), Yu.I. Manin, A.A. Panchishkin, Encyclopaedia of Mathematical Sciences, 49, 2005, Springer
• On weak automorphs of binary forms over an arbitrary field, Andrzej Schinzel, Dissertationes Mathematicae 434, 2005
• Complex analysis, Eberhard Freitag, Rolf Busam, Springer 2005
• Sums of Squares of Integers, Carlos J. Moreno, Samuel S. Wagstaff, Jr., Discrete Mathematics and Its Applications 37, CRC Press 2005
• Formes Automorphes (II): Le Cas Du Groupe GSp(4), Ed. Jacques Tilouine, Henri Carayol, Michael Harris and Marie-France Vigneras, Astérisque 302, 2005
• Spectre Automorphe des Variétés Hyperboliques et Applications Topologiques, Nicolas Bergeron, Laurent Clozel, Astérisque 303, 2005
• Number Fields and Function Fields: Two Parallel Worlds, Progress in Mathematics 239, Birkhäuser 2005
• Automorphic forms and shimura varieties of PGSp(2), Yuval Flicker, World Scientific, 2005
• Frontiers in Number Theory, Physics, and Geometry I, P. Cartier, B. Julia, P. Moussa, P. Vanhove, (Eds.) Springer 2005
• History of the Theory of Numbers Leonard Eugene Dickson, Dover reprint, 2005
• Recent Perspectives in Random Matrix Theory and Number Theory, Ed. F. Mezzadri, Nina Snaith, LMS Lecture notes 322, CUP 2005
• Moments, monodromy, and perversity: Diophantine perspective, Nicholas Katz, Annals of Mathematics Studies 159, 2005, PUP, review by Michael Larsen

Number Theory Books, 2006

• Cyclotomic Fields and Zeta Values, John Coates, Ramdorai Sujatha, Springer Monographs in Mathematics, 2006
• Thèmes d'arithmétique - Avec plus de 85 exercices corrigés, Olivier Bordellès, Ellipses Marketing, 2006
• Automorphic Forms and L-Functions for the Group GL(n,R), Dorian Goldfeld, CUP, 2006
• Automorphic forms and zeta functions: Proceedings of a Conference in Memory of Tsuneo Arakawa, Ed. Siegfried Böcherer, Tomoyoshi Ibukiyama, Masanobu Kaneko, Fumihiro Sato , World Scientific 2006
• Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory, Alfred Geroldinger and Franz Halter-Koch, Chapman & Hall/CRC 2006
• An Invitation to Modern Number Theory, Steven Miller, Ramin Takloo-Bighash, Princeton University Press 2006
• One Semester of Elliptic Curves, Torsten Ekedahl, AMS 2006
• Number Theory: An Introduction via the Distribution of Primes, Benjamin Fine, Gerhard Rosenberger, Birkhäuser 2006
• Number Theory: A Problem-Solving Approach, Titu Andreescu, Dorin Andrica, Birkhäuser 2006
• Numeri e Crittografia, Stefano Leonesi, Carlo Toffalori, Springer 2006
• Number Theory: Tradition and Modernization, Ed. Wenpeng Zhang, Yoshio Tanigawa, Developments in Mathematics 15 Springer 2006
• Valuations, Orderings, and Milnor K-Theory, Ido Efrat, Mathematical Surveys and Monographs 124, AMS 2006
• Helmut Hasse und Emmy Noether, Die Korrespondenz 1925-1935, Commentary by Franz Lemmermeyer and Peter Roquette, Universitätsverlag Göttingen 2006
• Multiplicative Number Theory I, H.L. Montgomery, R.C. Vaughan, Cambridge Studies in Advanced Mathematics 97, CUP, September 2006
• Algebraic Numbers and Algebraic Functions, Emil Artin, Chelsea Publishing 2006
• Number Theory in the Spirit of Ramanujan, Bruce Berndt, AMS Student Mathematical Library 34 (September) 2006
• Noncommutative Geometry and Number Theory: Where Arithmetic meets Geometry and Physics, Ed. Caterina Consani, Matilde Marcolli, Vieweg Aspects of Mathematics 37 2006
• Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory, Ed. Solomon Friedberg, Daniel Bump, Dorian Goldfeld, Jeffrey Hoffstein, Proceedings of Symposia in Pure Mathematics 75, AMS, Dec 2006
• Topics in the Theory of Algebraic Function Fields, Gabriel Daniel Villa Salvador, Birkhäuser 2006
• Algebraic Geometry and Number Theory: In Honor of Vladimir Drinfeld's 50th Birthday, Progress in Mathematics 253, Birkhäuser 2006
• Additive Combinatorics, Terence Tao, Van H. Vu, Cambridge Studies in Advanced Mathematics 105, CUP 2006
• Elliptic functions, J.V. Armitage, W.F. Eberlein, London Mathematical Society Student Texts 67, CUP 2006
• Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields, Alexandra Shlapentokh, New Mathematical Monographs 7, CUP November 2006
• The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae, (Ed.) Catherine Goldstein, Norbert Schappacher, Joachim Schwermer, Springer 2006
• Automorphic representations of low rank groups, Yuval Flicker, World Scientific, 2006
• The Local Langlands Conjecture for GL(2), Colin Bushnell, Guy Henniart, Grundlehren der mathematischen Wissenschaften, 335 , Springer 2006
• Heights in Diophantine Geometry, Enrico Bombieri, Walter Gubler, New Mathematical Monographs 4, CUP 2006
• Hilbert Modular Forms and Iwasawa Theory, Haruzo Hida, OUP 2006
• Elliptic Curves, James S. Milne, Booksurge Publishing 2006
• Arithmetic Duality Theorems, James S. Milne, Booksurge Publishing 2006
• A Collection of Manuscripts Written in Honour of John H. Coates on the Occasion of His Sixtieth Birthday, Ed. Ivan Fesenko, Stephen Lichtenbaum, Bernadette Perrin-Riou, Peter Schneider, Documenta Mathematica 4, 2006
• Selmer Complexes, Jan Nekovář, Astérisque 310, 2006
• Ultrametric calculus: an introduction to p-adic analysis, W.H. Schikhof, Cambridge Studies in Advanced Mathematics 4, CUP 2006

  Number Theory Books, 2007

• Introduction to Number Theory, Martin Erickson, Tony Vazzana, CRC Press 2007
• Eisenstein Series and Applications, Wee Teck Gan, Stephen S. Kudla, Yuri Tschinkel (Eds.) Progress in Mathematics 258, Birkhäuser 2007
• Traces of Hecke Operators, Andrew Knightly, Charles Li, AMS Mathematical Surveys and Monographs 133, January 2007
• Value Distributions of L-Functions, Jörn Steuding, Lecture Notes in Mathematics 1877, Springer, April 2007
• Modular Forms, a Computational Approach, William Stein, Graduate Studies in Mathematics 79, AMS March 2007
  • Modular Forms: A Computational Approach, by William Stein (2007), is now downloadable
• Hypergéométrie et Fonction Zêta de Riemann, Christian Krattenthaler, Tanguy Rivoal, Memoirs of the American Mathematical Society 186, February 2007
• 1001 Problems in Classical Number Theory, Jean-Marie De Koninck, Armel Mercier, AMS May 2007
• The Conference on L-functions, Fukuoka, February 18-23 2006, Ed. Lin Weng, Masanobu Kaneko, World Scientific 2007
• Arithmetic geometry and number theory, Ed. Lin Weng, Iku Nakamura, Series on Number Theory and its application 1
• Number Theory: An Introduction via the Distribution of Primes, Benjamin Fine, Gerhard Rosenberger, Birkhäuser 2007 (warning: pages 121-152 were upside down in the UQ library copy!)
• Automorphic Forms and Applications, Ed. Peter Sarnak, Freydoon Shahidi, AS/Park City Mathematics Series, 12, AMS, 2007
• Andrzej Schinzel, Selecta, Ed. Henryk Iwaniec, Władysław Narkiewicz, Jerzy Urbanowicz, Heritage of European Mathematics Series, Volume 1, European Mathematical Society Publishing House 2007
• Number Theory Vol I: Tools and Diophantine Equations Vol II: Analytic and Modern Tools, Henri Cohen, Springer-Verlag - Graduate Texts in Mathematics 239 and 240, May 2007, Errata (pdf)
• Equidistribution in Number Theory, An Introduction, Proceedings of the NATO Advanced Study Institute on Equidistribution in Number Theory, Montreal, Canada, 11-22 July 2005, ed. Andrew Granville, Zeev Rudnick, NATO Science Series II: Mathematics, Physics and Chemistry 237, Springer 2007
• Combinatorial number theory, Proceedings of the 'Integers Conference 2005' in Celebration of the 70th Birthday of Ronald Graham, Carrollton, Georgia, October 27-30, 2005, Ed. Bruce Landman, Melvyn Nathanson, Jaroslav Nešetril, Richard Nowakowski, Carl Pomerance, Proceedings in Mathematics, 2007, Walter de Gruyter
• The Arithmetic of Dynamical Systems, J.H. Silverman, Springer-Verlag Graduate Text 241, Spring 2007
• Elementary Number Theory, Jie Xiao, International Press 2007
• 104 Number Theory Problems (From the Training of the USA IMO Team), Titu Andreescu, Dorin Andrica, Zuming Feng, Birkhäuser 2007
• Sur les courbes hyperelliptiques cyclotomiques et les équations x^p-y^p=cz², Wilfrid Ivorra, Dissertationes Math. 444 (2007), 1-46
• Binary Quadratic Forms: An Algorithmic Approach, Johannes Buchmann, Ulrich Vollmer, Algorithms and Computation in Mathematics , 20, Springer 2007
• Prime-Detecting Sieves, Glyn Harman, Princeton University Press 2007
• Experimental Number Theory, Fernando Rodriguez Villegas, Oxford Graduate Texts in Mathematics number 13, OUP 2007
• Probability and Number Theory-Kanazawa 2005, Shigeki Akiyama, Kohji Matsumoto, Leo Murata, Hiroshi Sugita, Advanced Studies in Pure Mathematics, 49, AMS, 2007
• Ranks of Elliptic Curves and Random Matrix Theory, Brian Conrey, David Farmer, F. Mezzadri, Nina Snaith, LMS Lecture notes 341, CUP 2007
• L-Functions and Galois Representations, Ed. David Burns, Kevin Buzzard, Jan Nekovář, LMS Lecture Notes 320 CUP 2007
• Elementare und algebraische Zahlentheorie, Stefan Müller-Stach, Jens Piontkowski, Vieweg, 2007
• More Math Into LaTeX, George Grätzer, Springer 2007 (very good!)
• Diophantine Equations, 2005 Mumbai conference in honour of T.N. Shorey, Ed: N. Saradha, Tata Institute of Fundamental Research, Mumbai, India, AMS 2007
• Hecke's theory of modular forms and Dirichlet series (2nd Printing with revisions), Bruce Berndt, Marvin Knopp, Monographs in Mathematics 5, World Scientific 2007
• $p$-adic Analysis Compared with Real, Svetlana Katok, AMS Student Mathematical Library 37 2007, Errata
• Number-Theoretic Algorithms in Cryptography, Oleg Vasilenko, Translations of Mathematical Monographs 232, AMS 2007

Number Theory Books, 2008

• Kono teiri ga utsukushii (These are beautiful theorems) and Sugaku-no-Tanoshimi (Have Fun with Mathematics)
• Class Field Theory, Nancy Childress, Universitext, Springer, December 2008
• Higher Arithmetic: An Algorithmic Introduction to Number Theory, Harold M. Edwards, Student Mathematical Library 45, AMS 2008
• The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, P. Borwein, S. Choi, B. Rooney, A. Weirathmueller (Eds.), CMS Books in Mathematics XIV, 2008, Springer
• Basic Quadratic Forms, Larry Gerstein, Graduate Studies in Mathematics 90, AMS, May 2008
• Elliptic Curves and Big Galois Representations, Daniel Delbourgo, LMS Lecture Notes 356, CUP June 2008
• Number Theory and Polynomials, Ed. James McKee, Chris Smyth, LMS Lecture notes 352, CUP May 2008
• Theory of Numbers, Amin Witno, BookSurge Publishing 2008
• The Large Sieve and its Applications, Arithmetic Geometry, Random Walks and Discrete Groups, Emmanuel Kowalski, Cambridge Tracts in Mathematics (No. 175) CUP 2008
• A Tribute to Paul Erdös, Ed. Alan Baker, Bela Bollabás, Andras Hajnal, CUP 2008
• p-adic Geometry: Lectures from the 2007 Arizona Winter School, ed. David Savitt and Dinesh S. Thakur, University Lecture Series 45 September 2008
• Anatomy of Integers, Ed. Jean-Marie De Koninck, Andrew Granville, Florian Luca, CRM Proceedings & Lecture Notes, 46, August 2008
• Modular Forms on Schiermonnikoog, Ed. Bas Edixhoven, Gerard van der Geer, Ben Moonen, CUP 2008
• Modular forms, a classical and computational introduction,Lloyd Kilford, World Scientific, Fall 2008
• Computational Arithmetic Geometry, Ed. Kristin E. Lauter, Ken Ribet, Contemporary Mathematics 463, August 2008
• Surveys in Number Theory, Ed. Krishnaswami Alladi, Developments in Mathematics, 17 Springer, September 2008
• Diophantine Analysis and Related Fields, DARF2007/2008, Ed. Takao Komatsu, AIP Conference Proceedings, Vol. 976, 2008
• Distribution Theory of Algebraic Numbers, Hu, Pei-Chu & Yang, Chung-Chun, Series: de Gruyter Expositions in Mathematics 45 November 2008
• Fundamental number theory with applications, Richard Mollin, CRC Press 2008
• Elliptic Curves: Number Theory and Cryptography, (second edition) Lawrence C. Washington, Chapman Hall/CRC 2008
• An Introduction to the Theory of Numbers, Sixth Edition, G.H. Hardy and E.M. Wright, Edited by Roger Heath-Brown and Joseph Silverman, Foreward by Andrew Wiles, OUP 2008
  • Misprints in Hardy & Wright (6th edition), and in Titchmarsh (2nd edition)
• Distribution Theory of Algebraic Numbers, Hu, Pei-Chu and Yang, Chung-Chun, de Gruyter Expositions in Mathematics 45, 2008
• A Higher-Dimensional Sieve Method With Procedures for Computing Sieve Functions, Harold Diamond, Heini Halberstam, Will Galway, Cambridge Tracts in Mathematics 177, 2008
• Random Curves: Journeys of a Mathematician, Neal Koblitz, Springer 2008
• The Map of My Life, Goro Shimura, Springer 2008
  • Comments on The Map of My Life
  • Review by Fernando Q. Gouvêa of Goro Shimura's The Map of My Life
• Emil Artin und Helmut Hasse: Die Korrespondenz 1923-1934, Günter Frei, Peter Roquette, with assistance from Franz Lemmermeyer, Universitätsverlag Göttingen 2008, Online version; Review by Javier Fresán;
• Algebraic Function Fields and Codes, Henning Stichtenoth, Graduate Text 254, Springer 2008
• The 1-2-3 of Modular Forms, Bruinier, J.H., van der Geer, G., Harder, G., Zagier, D., Springer Universitext 2008
  • The 1-2-3 of modular forms reviewed by Amanda Folsom , Bull. Amer. Math. Soc. 46 (2009), 527-533
• Dreaming in Dreams, Proceedings of the 5th China-Japan Seminar, Higashi-Osaka, Japan, 27-31 August 2008, edited by Takashi Aoki, Shigeru Kanemitsu and Jianya Liu, World Scientific 2009
• Algorithmic Number Theory, Edited by Joe P. Buhler and Peter Stevenhagen, Mathematical Sciences Research Institute Publications, December 2008 CUP, also see Preliminary version
• Logarithmic Forms and Diophantine Geometry, Alan Baker, Gisbert Wüstholz, New Mathematical Monographs (No. 9), CUP 2008
• Fearless Symmetry: Exposing the Hidden Patterns of Numbers, Avner Ash & Robert Gross, Princeton University Press 2008, MAA review of Fearless Symmetry: Exposing the Hidden Patterns of Numbers

Number Theory Books, 2009

• Cohomological Theory of Crystals over Function Fields, Gebhard Böckle and Richard Pink, EMS Tracts in Mathematics Vol. 9, 2009
• Algorithmic Number Theory , Ken Nakamula, 2009
• Solving the Pell Equation, Michael Jacobson Jr., Hugh Williams, CMS Books in Mathematics, Springer 2009
  • Review by Hendrik Lenstra and Peter Stevenhagen
• Post Quantum Cryptography, Ed. Dan Bernstein, Johannes Buchmann, Erik Dahmen, Springer 2009
• Catalan's Conjecture, René Schoof, Universitext, Springer 2009
• Ramanujan's Lost Notebook, Part II, Bruce Berndt, George Andrews, Springer January 2009
• Analytic Number Theory, Essays in Honour of Klaus Roth, Ed. William Chen, Timothy Gowers, Heini Halberstam, Wolfgang Schmidt, Robert Vaughan, CUP 2009
• Class Field Theory, Nancy Childress, Universitext, Springer 2009
• Elementary Number Theory: Primes, Congruences, and Secrets, William Stein, Undergraduate Text, Springer 2009 (freely available online)
• Elementary Number Theory, Cryptography and Codes, Maria Welleda Baldoni, Ciro Ciliberto, Cattaneo Piacentini, Maria Giulia, Universitext, Springer 2009
• Representations $p$-adiques de Groupes $p$-adiques I: Representations Galoisiennes et $(ϕ)$-Modules, Edited by: Laurent Berger, Christophe Breuil, Pierre Colmez, Astérisque 319, 2008
• Arithmetical Aspects of the Large Sieve Inequality, Olivier Ramaré, D. Surya Ramana, Hindustan Book Agency, 2009
• Modular Forms: A Computational Approach, by William Stein (2007), is now downloadable
• Analytic Number Theory for Undergraduates, Heng Huat Chan, Monographs in Number Theory, Vol. 3, World Scientific, 2009
• Analysis in Positive Characteristic, Anatoly N. Kochubei, Cambridge Tracts in Mathematics 178, CUP, 2009
• Introduction to Siegel Modular Forms and Dirichlet Series, Anatoli Andrianov, Universitext, Springer 2009
• Combinatorial Number Theory, Proceedings of the Integers Conference 2007, Carrollton, Georgia, USA, October 24-27, 2007, Ed. Bruce Landman, Melvyn Nathanson, Jaroslav Nešetril, Richard Nowakowski, Carl Pomerance, Aaron Robertson, de Gruyter 2009
• Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds, Rainer Weissauer, Lecture Notes in Mathematics 1968, Springer 2009
• Number Theory and Applications: Proceedings of the International Conferences on Number Theory and Cryptography, Edited by: S. D. Adhikari and B. Ramakrishnan, Hindustan Book Agency, July 2009
• Quadratic Forms-Algebra, Arithmetic, and Geometry, Ed. Ricardo Baeza, Wai Kiu Chan, Detlev W. Hoffmann, Rainer Schulze-Pillot, Contemporary Mathematics 493, AMS 2009
• Not Always Buried Deep: A Second Course in Elementary Number Theory, Paul Pollack, AMS November 2009, Errata
• Number Theory, An Introduction to Mathematics, W.A. Coppel, Universitext, Springer 2009
• Arithmetic Geometry, Ed. Henri Darmon, David Alexandre Ellwood, Brendan Hassett, Yuri Tschinkel, Clay Mathematics Proceedings, November 2009
• The Legacy of Leonhard Euler: A Tricentennial Tribute, Lokenath Debnath, Imperial College Press, October 2009
• Problems of Number Theory in Mathematical Competitions, Yu Hong-Bing, World Scientific, September 2009
• Mathematicians: An Outer View of the Inner World, Mariana Cook, Princeton University Press 2009, MAA review
• Algebraic Number Theory and Related Topics 2007, Eds. M. Asada, H. Nakamura and H. Takahashi, RIMS, Kôkyûroku Bessatsu B12, August, 2009
• Those Fascinating Numbers, Jean-Marie De Koninck, AMS 2009
• Combinatorial Number Theory and Additive Group Theory, Alfred Geroldinger and Imre Z. Ruzsa, Birkhäuser 2009
• Algebraic Independence, Yu. V. Nesterenko, Narosa, 2009
• Biscuits of Number Theory, Ed. Ezra Brown, Arthur Benjamin, MAA, 2009
• Azar y aritmética, Harald Helfgott, Monografías del IMCA 51 2009

Number Theory Books, 2010

• Additive Number Theory, Ed. David Chudnovsky, Gregory Chudnovsky, Springer 2010
• The LLL Algorithm, Survey and Applications, Phong Nguyen, Brigitte Valleé, Springer 2010
• Opera de Cribro, John Friedlander, Henryk Iwaniec, Vol 57, AMS Colloquium Publication, May 2010
• LMS republishes Cassels and Fröhlich, Errata
• Automorphic Forms and the Langlands Program, Edited by: Lizhen Ji, Kefeng Liu, Shing-Tung Yau, Zhu-Jun Zheng, International Press 2010
• Eisenstein Series and Automorphic L-Functions, Freydoon Shahidi, AMS Colloquium Publications 58, 2010 (not yet published)
• Complex multiplication, Reinhard Schertz, New Mathematical Monographs (No. 15), CUP, 2010
• Arithmetic, Geometry, Cryptography and Coding Theory 2009, Edited by: David Kohel and Robert Rolland, Contemporary Mathematics 521, September 2010
• p-adic Differential Equations, Kiran Kedlaya, Series: Cambridge Studies in Advanced Mathematics (No. 125) CUP, 2010
  • Review of p-adic differential equations, by Kiran Kedlaya, Reviewer: Laurent Berger
• Galois Cohomology of Elliptic Curves: Second Edition, John Coates, R. Sujatha (publication of the Tata Institute of Fundamental Research)
• Arithmetic of Quadratic Forms, Goro Shimura, Springer Monographs in Mathematics XII, 2010
• Number Theory, An Elementary Introduction Through Diophantine Problems, Daniel Duverney, Monographs in Number Theory - Vol. 4, World Scientific, 2010
• Automorphe Formen, Anton Deitmar, Springer-Lehrbuch Masterclass VII, 2010
• Advanced Number Theory with Applications, Richard Mollin, CRC Press, Taylor and Francis, 2009
• Algebraic Curves and Cryptography, Edited by: V. Kumar Murty, Fields Institute Communications, 58, AMS 2010
• Arithmetic Geometry, Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007, Jean-Louis Colliot-Thélène, Peter Swinnerton-Dyer, Paul Vojta, Pietro Corvaja, Carlo Gasbarri (Eds.), Lecture Notes in Mathematics, Vol. 2009, 2010
• Combinatorics, Automata and Number Theory, Ed. Valérie Berthé, Michel Rigo, CUP 2010
• Number Theory in the Spirit of Liouville, Kenneth S. Williams, London Mathematical Society Student Texts (No. 76) 2010
• Zeta Functions of Graphs, Audrey Terras, Cambridge Studies in Advanced Mathematics (No. 128) 2010, Review by Laurent Bartholdi
• Modern Computer Arithmetic, Richard Brent and Paul Zimmermann, Cambridge University Press, 2010
• Algebraic and Analytic Aspects of Zeta Functions and L-functions, MSJ Memoirs, vol. 21, G. Bhowmik, K. Matsumoto and H. Tsumura (eds.), Mathematical Society of Japan, 2010
• The Ultimate Challenge: The $3x+1$ Problem, Ed. Jeffrey C. Lagarias, AMS January 2010, Review by Darren Glass
• Zeta Functions over Zeros of Zeta Functions, André Voros, Lecture Notes of the Unione Matematica Italiana, Vol. 8, Springer 2010
• Number Theory: A Lively Introduction with Proofs, Applications, and Stories, Jamie Pommersheim, Tim Marks, Erica Flapan, Wiley 2010

Number Theory Books, 2011

• Galois Module Structure of the Group of Units of Real Abelian Fields, Roman Marszałek, Studia I Monografie Nr 465, 2011
• Diophantine Analysis and Related Fields 2011: DARF - 2011, Ed. Masaaki Amou, Masanori Katsurada, AIP, 2011
• Eta Products and Theta Series Identities, Günter Köhler, Springer Monographs in Mathematics, 2011
• Elliptic Curves, Modular Forms, and Their L-functions, Alvaro Lozano-Robledo, Student Mathematical Library 58, 2011, AMS, MAA Review by Michael Berg
• WIN-Women in Numbers: Research Directions in Number Theory, Ed. Alina-Carmen Cojocaru, Rachel Pries, Renate Scheidler, Fields Institute Communications 60, AMS March 2011
• At Home with André and Simone Weil, Sylvie Weil, Northwestern University Press, 2010, Book review by Michèle Audin, Notices of the AMS, May 2011
• New developments in the additive theory of prime numbers, Jianya Liu, Tao Zhan, World Scientific 2015
• An invitation to q-series: from Jacobi's triple product identity to Ramanujan's most beautiful identity, Hei-Chi Chan, World Scientific, 2011
• Iwasawa Theory, Projective Modules, and Modular Representations, Ralph Greenberg, 211, Memoirs of the American Mathematical Society, 2011
• On Certain $L$-Functions, Ed. James Arthur, James Cogdell, Steve Gelbart, David Goldberg, Dinikar Ramakrishnan, Jiu-Kang Yu, 13, Clay Mathematics Proceedings, 2011
• Collected Works of Hervé Jacquet, Ed. Dorian Goldfeld, AMS Collected Works , Volume 23, 2011
• Dynamical Systems and Diophantine Approximation, Ed. Yann Bugeaud, Françoise Dal'Bo, Cornelia Druţu, Séminaires et Congrès, Volume 19, 2011
• Arithmetic of $L$-functions, Ed. Cristian Popescu, Karl Rubin and Alice Silverberg, Volume 18, IAS/Park City Mathematics Series, AMS 2011
• Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), World Scientific 2011
• Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications, Murray R. Bremner, CRC Press 2011
• Rational Number Theory in the 20th Century, Władysław Narkiewicz, Springer 2012
• Dover Publications has just re-issued Halberstam and Richert's classic Sieve Methods.
• Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime, Ed. Bas Edixhoven & Jean-Marc Couveignes, with Robin de Jong, Franz Merkl & Johan Bosman
• Geometric modular forms and elliptic curves, (second edition) Haruzo Hida, World Scientific, 2011, MAA Review by Michael Berg
• On Certain L-Functions, Eds. J. Arthur, J.W. Cogdell, S. Gelbart, D. Goldberg, D. Ramakrishnan, J.-K. Yu, CMI/AMS publication, 2011
• Automorphic Representations and L-Functions for the General Linear Group, Vol. 1, Dorian Goldfeld and Joseph Hundley, Cambridge Studies in Advanced Mathematics 129, 2011
• Automorphic Representations and L-Functions for the General Linear Group, Vol. 2, Dorian Goldfeld and Joseph Hundley, Cambridge Studies in Advanced Mathematics 130, 2011
• Analytic Number Theory. vol.1. The distribution of prime numbers, Yoichi Motohashi, Asakura Books, Tokyo 2009. ISBN 978-4-254-11821-6 (translation into English being undertaken)
• Analytic Number Theory. vol.2. The zeta analysis, Yoichi Motohashi, Asakura Books, Tokyo 2009. ISBN 978-4-254-11822-3 (translation into English being undertaken)
• Problem-Solving and Selected Topics in Number Theory in the Spirit of the Mathematical Olympiads, Michael Rassias, Springer 2011
• Lectures on N_X(p), Jean-Pierre Serre, CRC Press 2011
• Number Theory 2: Introduction to Class Field Theory, Kazuya Kato, Nobushige Kurokawa, Takeshi Saito, Translations of Mathematical Monographs Vol 240, AMS 2011
• Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory, Ben Brubaker, Daniel Bump, Solomon Friedberg, Annals of Mathematics Studies Vol. 175, Princeton University Press 2011
• Development of Elliptic Functions According to Ramanujan, K. Venkatachaliengar (edited by Shaun Cooper) Monographs in Number Theory: Volume 6, World Scientific, 2011
• Arithmetic and Galois Theories of Differential Equations, Ed. Lucia Di Vizio, Tanguy Rivoal, Séminaires et Congrès 23, 2011
• Arithmetics, Marc Hindry, Universitext, Springer 2011

Number Theory Books, 2012

• Contributions in Analytic and Algebraic Number Theory, Ed. Valentin Blomer, Preda Mihăilescu, Springer Proceedings in Mathematics 9, 2012
• Knots and Primes, Masanori Morishita, Springer 2012
• Partitions, q-Series, and Modular Forms, Ed. Krishnaswami Alladi, Frank Garvan, Series: Developments in Mathematics, Vol. 23, Springer 2012
• Elliptic Tales: Curves, Counting, and Number Theory, Avner Ash & Robert Gross, Princeton University Press, 2012
• Analytic Number Theory: Exploring the Anatomy of Integers, Jean-Marie De Koninck & Florian Luca, Graduate Studies in Mathematics, Number 134, AMS 2012
• Distribution Modulo One and Diophantine Approximation, Yann Bugeaud, Cambridge Tract 193, 2012
• Number Theory 3: Iwasawa Theory and Modular Forms, Nobushige Kurokawa, Masato Kurihara, Takeshi Saito, Translations of Mathematical Monographs 242, AMS 2012
• Some Problems of Unlikely Intersections in Arithmetic and Geometry, Umberto Zannier, with appendices by David Masser, Princeton University Press 2012, Review by Joe Silverman
• Higher Order Fourier Analysis, Terence Tao, AMS Graduate Studies in Mathematics 142, November 2012
• The Theory of Hardy's Z-Function, Aleksandar Ivić, Cambridge Tract in Mathematics 196, 2012
• Automorphic Forms, Anton Deitmar, Universitext, Springer 2012
• Six Short Chapters on Automorphic Forms and L-functions, Ze-Li Dou, Qiao Zhang, Springer 2012
• A Comprehensive Course in Number Theory, Alan Baker, CUP 2012
• Rational Points and Arithmetic of Fundamental Groups, Jakob Stix, Lecture Notes in Mathematics, Vol. 2054, 2012
• Mathematics of Public Key Cryptography, Steven Galbraith, Cambridge University Press, 2012
• Arithmetic Tales, Olivier Bordèlles, Universitext, Springer 2012
• Intersections of Hirzebruch-Zagier Divisors and CM Cycles, Benjamin Howard, Tonghai Yang, Lecture Notes in Mathematics, Vol. 2041, Springer 2012
• Zahlentheorie: Eine Einführung mit Übungen, Hinweisen und Lösungen , Martin Aigner, Reihe: Bachelorkurs Mathematik, Springer 2012
• Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms, Nicholas M. Katz, AM-180, Princeton University Press, 2012, Review by Emmanuel Kowalski
• Explicit Methods in Number Theory Rational Points and Diophantine Equations, Karim Belabas, Hendrik W. Lenstra Jr., Pierrick Gaudry, Michael Stoll, Mark Watkins, William McCallum & Bjorn Poonen, Frits Beukers, Samir Siksek, Panoramas et synthèses 36 (2012)
• Continued fractions and r/j-algorithm, V.I. Shmoylov, Rostov-on-Don: Publishing House of the Southern Federal University, 2012, 608 p.
• Introducción a la teoría de números, Felipe Zaldívar, 2012
• Galois-Teichmüller Theory and Arithmetic Geometry, Ed: Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa, Advanced Studies in Pure Mathematics: Volume 63, World Scientific, 2012

Number Theory Books, 2013

• Number Theory: Arithmetic in Shangri-La, Proceedings of the 6th China-Japan Seminar, Shanghai, China, 15-17 August 2011, edited by Shigeru Kanemitsu, Hongze Li and Jianya Liu, World Scientific 2013
• Modular Forms with Integral and Half-Integral Weights, Xueli Wang, Dingyi Pi, Springer 2013
• The Mathematical Legacy of Srinivasa Ramanujan, M. Ram Murty, V. Kumar Murty, Springer 2013
• Noncommutative Iwasawa Main Conjectures over Totally Real Fields, Ed. John Coates, Peter Schneider, Sujatha Ramdorai, Otmar Venjakob, Springer Proceedings in Mathematics & Statistics, Vol. 29, 2013
• Ramanujan's Place in the World of Mathematics, Krishnaswami Alladi, Birkhäuser 2013
• Drinfeld Moduli Schemes and Automorphic Forms, Yuval Flicker, SpringerBriefs in Mathematics, 2013
• Elliptic Curves, Hilbert Modular Forms and Galois Deformations, L. Berger, G. Böckle, L. Dembélé, M. Dimitrov, T. Dokchitser, J. Voight, Birkhäuser, 2013
• Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms, Wai Kiu Chan, Lenny Fukshansky, Rainer Schulze-Pillot, Jeffrey D. Vaaler, Contemporary Mathematics 587 AMS 2013
• Automorphic Representations and L-functions, D. Prasad, C. S. Rajan, A. Sankaranarayanan, J. Sengupta, Tata Institute of Fundamental Research, 2013
• Computational Number Theory, Abhijit Das, Chapman and Hall/CRC, 2013
• Number Theory and Related Fields, Ed. Jonathan Borwein, Igor Shparlinski, Wadim Zudilin, Springer Proceedings in Mathematics & Statistics, Vol. 43, 2013
• Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms, A. Knightly, C. Li, Memoirs of the American Mathematical Society 224, 2013
• Markov's Theorem and 100 Years of the Uniqueness Conjecture, Martin Aigner, Springer 2013
• Geometry of Continued Fractions, Oleg Karpenkov, Algorithms and Computation in Mathematics, Vol. 26, Springer 2013
• Quadratic and Higher Degree Forms, Krishnaswami Alladi, Manjul Bhargava, Dave Savitt, Pham Huu Tiep, Developments in Mathematics, Vol. 31, Springer 2013
• Quadratic Irrationals: An Introduction to Classical Number Theory, Franz Halter-Koch, CRC Press 2013
• Fermat's Last Theorem: Basic Tools, Takeshi Saito, Translations of Mathematical Monographs, Iwanami Series in Modern Mathematics 243, November 2013
• Elliptic Diophantine Equations: A Concrete Approach via the Elliptic Logarithm, Nikos Tzanakis, De Gruyter Series in Discrete Mathematics and Applications 2, 2013
• Women in Numbers 2: Research Directions in Number Theory, Ed. Chantal David, Matilde Lalin, Michelle Manes, Contemporary Mathematics Vol 606, AMS 2013
• Contributions to the History of Number Theory in the 20th Century, Peter Roquette, European Mathematical Society Publishing House, 2013
  • Review of Roquette's Contributions to the History of Number Theory in the 20th Century by Fernando Gouvêa
• Algebraic Theory of Quadratic Numbers, Mak Trifković, Universitext, Springer 2013
• Algebraic Curves in Cryptography, San Ling, Huaxiong Wang, Chaoping Xing, Discrete Mathematics and Its Applications, CRC Press 2013
• AUTOUR DES MOTIFS (II)- Asian-French summer school on algebraic geometry and number theory, Ed. Marc Lévine, Jörg Wildeshaus, Bruno Kahn, Panoramas et synthèses 41 (2013)
• Elliptic Curves and Arithmetic Invariants, Haruzo Hida, Springer Monograph in Mathematics, Springer 2013
• Erdös Centennial, Editors: Lázló Lovász, Imre Ruzsa, Vera Sós, Springer 2013
• Number Theory, Analysis, and Combinatorics, Proceedings of the Paul Turan Memorial Conference held August 22-26, 2011 in Budapes, De Gruyter Proceedings in Mathematics, 2013
• Los números trascendentes , Javier Fresán; Juanjo Rué, CSIC, Madrid, 2013
• Teoria dos Números Transcendentes, Diego Marques, SBM 2013

Number Theory Books, 2014

• Complex Multiplication and Lifting Problems, Ching-Li Chai, Brian Conrad, Frans Oort, Mathematical Surveys and Monographs 195, January 2014, AMS
• Computations with Modular Forms, Ed. Gebhard Böckle, Gabor Wiese, Contributions in Mathematical and Computational Sciences, Vol. 6, Springer 2014
• Emil Artin and Helmut Hasse, Ed. Günther Frei, Franz Lemmermeyer, Peter Roquette, Contributions in Mathematical and Computational Sciences, Vol. 5, Springer 2014
• Neverending Fractions, An Introduction to Continued Fractions, Jonathan Borwein, Alf van der Poorten, Jeffrey Shallit, Wadim Zudilin, CUP, 2014
• Zahlentheorie und Zahlenspiele: Sieben ausgewählte Themenstellungen, Hartmut Menzer, Ingo Althöfer, De Gruyter, 2014
• Pell and Pell-Lucas Numbers with Applications, Thomas Koshy, Springer 2014
• Algebraic Curves and Finite Fields Cryptography and Other Applications, Ed. Harald Niederreiter, Alina Ostafe, Daniel Panario, Arne Winterhof, Radon Series on Computational and Applied Mathematics 16, De Gruyter 2014
• Algebraic Number Theory, Frazer Jarvis, Springer Undergraduate Mathematics Series XIII, 2014, MAA review
• Transcendental Numbers, Ram Murty, Purusottam Rath, Springer, 2014
• Bernoulli Numbers and Zeta Functions, Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko, Springer Monographs in Mathematics XI, 2014
• Brauer Groups, Tamagawa Measures, and Rational Points on Algebraic Varieties, Jörg Jahnel, AMS Mathematical Surveys and Monographs 198, 2014
• The Problem of Catalan, Yuri Bilu, Yann Bugeaud, Maurice Mignotte, Springer, 2014,
• MAA Review of The Problem of Catalan
• Probabilistic Diophantine Approximation, József Beck, Springer Monographs in Mathematics, 2014
• A Panorama of Discrepancy Theory, Eds. William Chen, Anand Srivastav, Giancarlo Travaglini, Lecture Notes in Mathematics 2107, Springer 2014
• Arithmetic Geometry over Global Function Fields, Eds. Gebhard Böckle, David Goss, Dinesh Thakur, Douglas Ulmer, Francesc Bars, Ignazio Longhi, Fabien Trihan, Advanced Courses in Mathematics - CRM Barcelona, Birkhäuser, 2014
• Zahlentheorie und Zahlenspiele, Sieben ausgewählte Themenstellungen, Hartmut Menzer, Ingo Althöfer, De Gruyter 2014
• Early Fourier Analysis, Hugh Montgomery, Pure and Applied Undergraduate Texts 22, AMS 2014
• Elementary Number Theory, James S. Kraft, Larry Washington, CRC Press 2014
• Iwasawa Theory 2012, Eds. Thanasis Bouganis, Otmar Venjakob, Contributions in Mathematical and Computational Sciences, Vol. 7, Springer 2014,
• Automorphic Forms, Eds. B. Heim, M. Al-Baali, T. Ibukiyama, F. Rupp, Springer 2014
• Arakelov Geometry, Atsushi Moriwaki, Translations of Mathematical Monographs 244, AMS 2014
• On Some Applications of Diophantine Approximations, a translation of C.L. Siegel's Über einige Anwendungen diophantischer Approximationen, with a commentary by C. Fuchs and U. Zannier, Birkhäuser 2014
• A Course in Analytic Number Theory, Marius Overholt, Graduate Studies in Mathematics 160, AMS 2014
• Introductory Notes on Valuation Rings and Function Fields in One Variable, Renata Scognamillo, Umberto Zannier, Springer 2014
• The Riemann Hypothesis for Function Fields, Frobenius Flow and Shift Operators, Machiel van Frankenhuijsen, LMS Student Text 80, CUP 2014
• Nevanlinna Theory in Several Complex Variables and Diophantine Approximation, Junjiro Noguchi, Jörg Winkelmann, Springer 2014
• Lectures on the Riemann Zeta Function, Henryk Iwaniec, University Lecture Series 62, AMS 2014;
• Review by Brian Conrey of Henryk Iwaniec's book Lectures on the Riemann Zeta Function, Bulletin of the Amer. Math. Soc, January 2016
• Automorphic Forms and Galois Representations, Volume 1, Ed. Fred Diamond, Payman Kassaei, Minhyong Kim, London Mathematical Society Lecture Note Series 414, CUP 2014
• Automorphic Forms and Galois Representations, Volume 2, Ed. Fred Diamond, Payman Kassaei, Minhyong Kim, London Mathematical Society Lecture Note Series 415, CUP 2014
• Recorridos por la Teoría de Números, Juan Luis Varona, Electolibris and Real Sociedad Matemática Española, 2014 (the publishing house has closed permanently and the book is now available free for downloading.)
• Number Theory, an Historical Approach, John J. Watkins, Princeton University Press, 2014

Number Theory Books, 2015

• Einführung in Algebra und Zahlentheorie, Rainer Schulze-Pillot, Springer-Lehrbuch, 2015
• Algorithmische Zahlentheorie, Otto Forster, Second edition, Springer 2015
• Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields, Hatice Boylan, Lecture Notes in Mathematics, Vol. 2130, Springer 2015
• Introduction to Analytic and Probabilistic Number Theory, Gérald Tenenbaum, third edition, Graduate Studies in Mathematics 163, AMS 2015 MAA Review
• Problems in the Theory of Modular Forms, M. Ram Murty, Michael Dewar, Hester Graves, Hindustan Book Agency, 2015
• Emil Artin and Beyond - Class Field Theory and L-Functions, Della Dumbaugh and Joachim Schwermer, Heritage of European Mathematics, 9, 2015
• The Quadratic Reciprocity Law, a collection of classical proofs, Oswald Baumgart, Edited and Translated by Franz Lemmermeyer, Birkhäuser 2015, Review by Fernando Gouvêa
• Quadratic Diophantine Equations, Titu Andreescu, Dorin Andrica, Developments in Mathematics, Vol. 40, Springer 2015
• The Bloch-Kato Conjecture for the Riemann Zeta Function, John Coates, A. Raghuram, R. Sujatha, CUP 2015
• O-Minimality and Diophantine Geometry, Ed. G.O. Jones, A.J. Wilkie, CUP 2015
• Arithmetic and Geometry, Ed. Luis Dieulefait, D.R. Heath-Brown, Yu. V. Manin, B. Z. Moroz, Jean-Pierre Wintenberger, CUP 2015
• Unit Equations in Diophantine Number Theory, Jan-Hendrik Evertse, Kálmán Győry, CUP 2015, MAA Review of Unit Equations in Diophantine Number Theory
• Spectral Means of Central Values of Automorphic L-Functions for GL(2), Masao Tsuzuki, Memoirs of the American Mathematical Society, AMS 2015
• Period Functions for Maass Wave Forms and Cohomology, R. Bruggemann, J. Lewis, D. Zagier, Memoirs of the American Mathematical Society, AMS 2015
• Brandt Matrices and Theta Series over Global Function Fields, Chih-Yun Chuang, Ting-Fang Lee, Fu-Tsun Wei, Jing Yu, Memoirs of the American Mathematical Society, AMS 2015
• Analytic Number Theory In Honor of Helmut Maier's 60th Birthday, Ed. Carl Pomerance, Michael Rassias, Springer 2015
• Advances in the Theory of Numbers, Proceedings of the Thirteenth Conference of the Canadian Number Theory Association, Eds. Ayşe Alaca, Şaban Alaca, Kenneth Williams, Springer 2015
• CryptoSchool, Joachim von zur Gathen, Springer 2015
• Computing the Continuous Discretely, Integer-Point Enumeration in Polyhedra, Matthias Beck, Sinai Robins, Springer 2015
• Applied Number Theory, Harald Niederreiter, Arne Winterhof, Springer 2015
• Trends in number theory, Ed. Fernando Chamizo, Jordi Guàrdia, Antonio Rojas-León, José María Tornero, Contemporary Mathematics 649 2015, AMS
• Algebraic Number Theory and Fermat's Last Theorem, Ian Stewart, David Tall, Fourth Edition, 2015, CRC Press
• MAA Review of Famous Functions in Number Theory
• Sage for Undergraduates, Gregory V. Bard, AMS 2015
• Automorphic Forms and L-Functions for the Group GL(n,R), Dorian Goldfeld, Cambridge Studies in Advanced Mathematics 99, CUP 2015
• Sheaves and Functions Modulo p, Lectures on the Woods Hole Trace Formula, Lenny Taelman, London Mathematical Society Lecture Note Series 429, CUP 2015

Number Theory Books, 2016

• Dynamical Systems, Number Theory and Applications, A Festschrift in Honor of Armin Leutbecher's 80th Birthday, Edited by Thomas Hagen, Florian Rupp and Jürgen Scheurle, World Scientific, 2016
• My Search for Ramanujan, How I learned to count, Ken Ono, Amir Aczel, Springer 2016
• Collected Works of John Tate: Parts I and II, Ed. Barry Mazur, Jean-Pierre Serre, AMS 2016, Review of the Collected Works of John Tate (J.S. Milne)
• Advances in the Theory of Automorphic Forms and their L-functions, Dihua Jiang, Freydoon Shahidi, David Soudry, Contemporary Mathematics, Volume 664, AMS 2016
• Integral Points on Algebraic Varieties: An Introduction to Diophantine Geometry, Pietro Corvaja, Hindustan Book Agency, 2016
• Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures, Ed. David Kohel, Igor Shparlinski, Contemporary Mathematics, Volume 663, 2016, AMS
• Hilbert's Seventh Problem: Solutions and Extensions - See more at: https://bookstore.ams.org/hin-72, Robert Tubbs, Hindustan Book Agency, 2016
• Hilbert's Seventh Problem: Solutions and Extensions, Robert Tubbs, Springer 2016
• Summing It Up: From One Plus One to Modern Number Theory, Avner Ash & Robert Gross, Princeton University Press 2016, MAA Review by Mark Hunacek
• Prime Numbers and the Riemann Hypothesis, Barry Mazur, William Stein, CUP 2016, MAA Review
• Beurling Generalized Numbers, Harold Diamond, Wen-Bin Zhang, Mathematical Surveys and Monographs 213, AMS 2016
• Dynamics and Analytic Number Theory, Ed. Dzmitry Badziahin, Alexander Gorodnik, Norbert Peyerimhoff, LMS Lecture Note Series 457, CUP 2016
• Discriminant Equations in Diophantine Number Theory, Jan-Hendrik Evertse, Kálmán Győry, New Mathematical Monographs 32, CUP 2016
• Auxiliary Polynomials in Number Theory, David Masser, Cambridge Tracts in Mathematics 207, CUP 2016
• Unit equations in Diophantine number theory, Jan-Hendrik Evertse, Kálmán Győry, Cambridge Studies in Advanced Mathematics 146, CUP 2016, MAA Review
• Problems in the Theory of Modular Forms, M. Ram Murty, Michael Dewar, Hester Graves, Springer 2016
• Quadratic Residues and Non-Residues: Selected Topics, Steve Wright, Springer 2016
• Stabilisation de la formule des traces tordue, Volume 2, Colette Moeglin, Jean-Loup Waldspurger, Springer 2016
• The Book of Numbers, MAA Review, Tianxin Cai, World Scientific 2016
• The Riemann Hypothesis, Roland van der Veen and Jan van de Craats, MAA Press 2016
• Diophantine Analysis: Course Notes from a Summer School, Editor: Jön Steuding, Birkhäuser, 2016
• Collected Papers V of Goro Shimura, Ed. Alice Silverberg, Hiroyuki Yoshida, Springer, 2016
• Continued fractions: The Bibliography, Vladimir Shmoilov, Vladimir Voitulevich, Southern Federal University, Rostov-on-Don, USSR, 2016
• Autour des Motifs: Asian-French Summer School on Algebraic Geometry and Number Theory: Volume III, Takeshi Saito, Laurent Clozel, Jörg Wildehaus, Panoramas et Syntheses Vol. 49, AMS 2016
• An Introduction to Non-Abelian Class Field Theory: Automorphic Forms of Weight 1 and 2-Dimensional Galois Representations , Toyokazu Hiramatsu, Seiken Saito, World Scientific Series on Number Theory and Its Applications: Volume 13, 2016
• From Arithmetic to Zeta-Functions, Number Theory in Memory of Wolfgang Schwarz, Ed. Jürgen Sander, Jörn Steuding, Rasa Steuding, Springer, 2016
• On Dwork's p-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps, E. Delaygue, T. Rivoal, J. Roques, Memoirs of the American Mathematical Society, Vol. 246, No. 1163, AMS, 2016
• Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics, Springer 2016

Number Theory Books, 2017

• A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond ℤ, Paul Pollack, AMS Student Mathematical Library 84, 2017, MAA review
• Modern Cryptography and Elliptic Curves: A Beginner's Guide , Thomas Shemanske, AMS Student Mathematical Library 83, 2017, Review by Mark Hunacek
• An Illustrated Theory of Numbers, Martin H. Weissman, AMS 2017
• Around Langlands Correspondences, Ed. Farrell Brumley, Maria Paula Gómez Aparicio, Alberto Minguez, Contemporary Mathematics, Vol. 691, AMS 2017
• Periods and Special Functions in Transcendence, Paula Tretkoff, World Scientific 2017
• Number Theory - Diophantine Problems, Uniform Distribution and Applications, Ed. Christian Elsholtz, Peter Grabner, Springer 2017
• Rational Points on Varieties, Bjorn Poonen, AMS Graduate Studies in Mathematics, Volume 186, 2017
• Harmonic Maass Forms and Mock Modular Forms: Theory and Applications, Kathrin Bringmann, Amanda Folsom, Ken Ono, Larry Rolen, AMS Colloquium Publications Volume 64, 2017
• Goldbach's Problem, Michael Rassias, Springer 2017
• Ramanujan's Theta Functions, Shaun Cooper, Springer 2017, MAA Review by Michael Berg
• Equivalents of the Riemann hypothesis, Volume One: Arithmetic equivalents, Kevin Broughan, CUP 2017
• Equivalents of the Riemann hypothesis, Volume Two: Analytic equivalents, Kevin Broughan, CUP 2017
• Exploring the Riemann Zeta function, Hugh Montgomery, Ashkan Nikeghbali, and Michael Th. Rassias, editors, Springer 2017 , MAA review
• The Power of q, A Personal Journey, Michael Hirschorn, Springer 2017, Review by Allen Stenger
• Elliptic and Modular Functions from Gauss to Dedekind to Hecke, Ranjan Roy, CUP 2017, MAA Review by Michael Berg
• Closing the Gap, Vicky Neale, OUP, 2017
• Topics in Computational Number Theory Inspired by Peter L. Montgomery, Ed. Joppe W. Bos, Arjen K. Lenstra, CUP 2017
• Review of An Invitation to the Rogers-Ramanujan Identities, Andrew V. Sills, 2017, Reviewed by Krishnaswami Alladi

Number Theory Books, 2018

• Number Theory and Its Applications II, Hailong Li, Fuhuo Li, Shigeru Kanemitsu, World Scientific, 2018
• Linear Forms in Logarithms and Applications, Yann Bugeaud, IRMA Lectures in Mathematics and Theoretical Physics Vol. 28, 2018, Review by Allan Stenger
• Applications of Diophantine Approximation to Integral Points and Transcendence, Pietro Corvaja, Umberto Zannier, Cambridge Tract 212, 2018, MAA Review by Michael Berg
• Women in Numbers Europe II, Editors: Irene Bouw, Ekin Özman, Jennifer Johnson-Leung, Rachel Newton, Springer 2018
• Reassessing Riemann's Paper On the Number of Primes Less Than a Given Magnitude, Walter Dittrich, Springer, 2018
• Cubic fields with geometry, Sam A. Hambleton and Hugh C. Williams, Springer 2018
• Continued fractions and summation of series, V.I. Shmoylov, Ya.S. Korovin, D.Ya. Ivanov, Rostov-on-Don: SFU Publishing House, 2018
• Teoria dos números um passeio com primos e outros números familiares pelo mundo inteiro, Fabio Martinez, Carlos Gustavo Moreira, Nicolau Saldanha e Eduardo Tengan, IMPA 2018
• The Riemann Hypothesis in Characteristic p in Historical Perspective, Peter Roquette, Springer, 2018; MAA review by Fernando Gouvêa
• An Open Door to Number Theory, Duff Campbell, AMS/MAA Textbook, Volume 39, 2018
• Holomorphic Automorphic Forms and Cohomology, Roelof Bruggeman, Youngju Choie, Nikolaos Diamantis, Memoirs of the American Mathematical Society, Volume 253, No. 1212, AMS, 2018
• A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic, Ramin Takloo-Bighash, Springer, 2018
• An Experimental Introduction to Number Theory, Benjamin Hutz, American Mathematical Society, Pure and Applied Undergraduate Texts, Volume 31, 2018
• A Gentle Course in Local Class Field Theory Local Number Fields, Brauer Groups, Galois Cohomology, Pierre Guillot, CUP, 2018
• An Open Door to Number Theory, Duff Campbell, AMS/MAA Textbooks, Volume 39, 2018

Number Theory Books, 2019

• Mathematical Constants II, Steve Finch, CUP 2019
• The Story of Algebraic Numbers in the First Half of the 20th Century: From Hilbert to Tate, Władysław Narkiewicz, Springer 2019
• Zeta and L-functions in Number Theory and Combinatorics, Wen-Ching Winnie Li, CBMS Regional Conference Series in Mathematics, Volume 129, AMS, 2019
• Number Theory and Geometry: An Introduction to Arithmetic Geometry, Álvaro Lozano-Robledo, Pure and Applied Undergraduate Text, Volume 35, AMS, 2019,
• Arithmetic Geometry: Computation and Applications, Ed. Yves Aubry, Everett Howe, Christophe Ritzenthaler, Contemporary Mathematics, Volume 722, AMS, 2019, MAA Review
• Notes from the International Autumn School on Computational Number Theory, Ed. Ilker Inam, Engin Büyükaşik, Birkhäuser 2019
• The Computational and Theoretical Aspects of Elliptic Curves, Ed. Zhibin Liang, Chandrakant Aribam, Springer 2019
• A Torsion Jacquet-Langlands Correspondence, Frank Calegari, Akshay Venkatesh, Asterisque 409, AMS, 2019
• Siegel Modular Forms: A Classical and Representation-Theoretic Approach, Ameya Pitale, Springer, 2019
• On the class number of abelian number fields, Hasse's classic, translated by M. Hirabayashi, Springer, 2019
• Hecke's L-functions, Kenkichi Iwasawa, typeset from the original 1964 notes of the author, Springer, 2019
• Perfectoid Spaces: Lectures from the 2017 Arizona Winter School, Editors and authors, Bryden Cais, Bhargav Bhatt, Ana Caraiani, Kiran S. Kedlaya, Peter Scholze, Jared Weinstein, AMS Mathematical Surveys and Monographs 242, 2019
• A Course in Cryptography, Heiko Knospe, AMS Pure and Applied Undergraduate Texts 40, 2019
• Diophantine Equations and Power Integral Bases (Theory and Algorithms), István Gaál, Birkhaüser, 2019 (new, substantially extended second edition)
• Arithmetic and Geometry: Ten Years in Alpbach, Ed. Gisbert Wüstholz, Clemens Fuchs, Annals of Mathematics Studies 202, Princeton University Press, 2019
• Eisenstein Cohomology for GL_N and the Special Values of Rankin-Selberg L-Functions, Anantharam Raghuram, Günter Harder, Annals of Mathematics Studies 203, Princeton University Press, 2019
• The Distribution of Prime Numbers, Dimitris Koukoulopoulos, Graduate Studies in Mathematics, Volume 203, 2019
• Variations on a Theorem of Tate, Stefan Patrikis, Memoirs of the American Mathematical Society, Volume 1238, 2019
• Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic, J.L. Lehman, AMS Dolciani Mathematical Expositions, 52, 2019; Review by Fernando Q. Gouvêa
• Number Theory Revealed: An Introduction, Andrew Granville, AMS Textbook, 2019
• Analytic Methods in Arithmetic Geometry, Ed. Alina Bucur, David Zureick-Brown, AMS Contemporary Mathematics, Volume: 740, 2019
• Automorphic Forms and Related Topics, Ed. Samuele Anni, Jay Jorgenson, Lejla Smajlović, Lynne Walling, AMS Contemporary Mathematics, Volume 732, 2019
• Algebraic Curves and Their Applications, Ed. Lubjana Beshaj, Tony Shaska, AMS Contemporary Mathematics, Volume 724, 2019
• Number Theory Revealed: A Masterclass, Andrew Granville, Miscellaneous Books, Vol. 127, AMS, 2019
• Documenta Mathematica, Extra Vol., Mahler Selecta (2019) eLibM, also see bottom of Michael Baake's page
• Recorridos por la Teoría de Números, Juan Luis Varona, second edition 2019, Electolibris

Number Theory Books, 2020

• Class Groups of Number Fields and Related Topics , Ed. Kalyan Chakraborty, Azizul Hoque and Prem Prakash Pandey, Springer, 2020
• The Unity of Combinatorics, Ezra Brown, Richard Guy, The Carus Mathematical Monographs, Volume 36, 2020
• Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules, Laurent Berger, Peter Schneider, Bingyong Xie, Memoirs of the American Mathematical Society, Volume 1275, 2020
• Shimura Varieties, Ed. Thomas Haines, Michael Harris, LMS Lecture Notes 457, 2020
• Berkeley Lectures on p-adic Geometry, Peter Scholze, Jared Weinstein, Annals of Mathematics Studies Volume 207, 2020
• Galois Cohomology and Class Field Theory, David Harari, Springer Universitext, 2020
• Many Variations of Mahler Measures: A Lasting Symphony, François Brunault, Wadim Zudilin, CUP, 2020
• Third edition of p-adic Numbers: An Introduction, Fernando Gouvêa, MAA Review by Allen Stenger
• The Great Prime Number Race, Roger Plymen, AMS Student Mathematical Library, Volume 92, 2020
• Various Aspects of Multiple Zeta Functions: In Honor of Professor Kohji Matsumoto's 60th Birthday, Edited by Hidehiko Mishou, Takashi Nakamura, Masatoshi Suzuki, Yumiko Umegaki, AMS Advanced Studies in Pure Mathematics, Volume 84, 2020
• Davenport-Zannier Polynomials and Dessins d'Enfants, Nikolai M. Adrianov, Fedor Pakovich, Alexander K. Zvonkin, AMS Mathematical Surveys and Monographs, Volume 249, 2020
• Complex Analysis with Applications to Number Theory, T.N. Shorey, Springer 2020
• An Invitation To Algebraic Numbers And Algebraic Functions, Franz Halter-Koch, Chapman and Hall/CRC, 2020, MAA Review by Michael Berg
• Development Of Iwasawa Theory: The Centennial of K. Iwasawa's Birth, Ed. Masato Kurihara, Kenichi Bannai, Tadashi Ochiai, Takeshi Tsuji, Advanced Studies in Pure Mathematics, Vol. 86, 2020
• Arithmetic Tales, Advanced Edition, Olivier Bordellès, Springer 2020
• Number Theory, Róbert Freud, Edit Gyarmati, Pure and Applied Undergraduate Texts, Vol. 48, AMS 2020, An Introduction to q-analysis, Warren P. Johnson, Textbook, AMS 2020, MAA Review by Karl-Dieter Crisman
• Rational Points on Curves Over Finite Fields, Jean-Pierre Serre, Documenta Mathématiques, Vol. 18, Société Mathématique de France 2020
• A Journey Through The Realm of Numbers, Menny Aka, Manfred Einsiedler, Thomas Ward, Springer Undergraduate Mathematics Series, 2020, MAA review

Number Theory Books, 2021

• Number Theory, Andrej Dujella, Zagreb, 2021, MAA review , Review by Jean-Paul Allouche
• Bounded gaps between primes: the epic breakthroughs of the early 21st century, Kevin Broughan, CUP 2021, 576p+xiv
• Abelian Varieties and Number Theory, Ed. Moshe Jarden, Tony Shaska, Contemporary Mathematics, Volume 767, AMS 2021
• p-Adic Heights and p-Adic Hodge Theory, Denis Benois, Memoires de la Société Mathématique de France, Vol. 167, 2021
• An introduction to probabilistic number theory, Emmanuel Kowalski, CUP 2021
• Srinivasa Ramanujan: Life and Work of a Natural Mathematical Genius, Swayambhu, K. Srinivasa Rao, Springer 2021
• Lie Groups, Number Theory, and Vertex Algebras, Ed. Dražen Adamović, Andrej Dujella, Antun Milas, Pavle Pandžić, Contemporary Mathematics, Vol. 768, AMS 2021
• Steps into Analytic Number Theory: A Problem-Based Introduction, Paul Pollack, Akash Singha Roy, Problem Books in Mathematics, Springer, 2021,
• Review by Allen Stenger
• New Conjectures in Number Theory and Combinatorics (in Chinese), Zhi-Wei Sun, Harbin Institute of Technology Press, 2021, ISBN:978-7-5603-4378-5. This book consists of 13 chapters, and contains 820 open conjectures in number theory and combinatorics posed by the author.
• Elementary Modular Iwasawa Theory, Haruzo Hida, World Scientific, Series on Number Theory and Its Applications: Volume 16, 2021
• A Modern Introduction to Classical Number Theory, Tianxin Cai, World Scientific 2021
• Quaternion algebras, John Voight, Graduate Texts in Mathematics 288, Springer 2021, MAA review
• Around the unit circle, James McKee, Chris Smyth, Springer Universitext, 2021
• Irrationality and Transcendence in Number Theory, David Angell, Taylor and Francis 2021

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Last modified 19th April 2022