Recommended Number Theory Books for Master’s and Ph.D. Students:
Alan Baker, A Concise Introduction to the Theory of Numbers. Springer, 1984, 174 pages.
Duncan A. Buell, Binary Quadratic Forms: Classical Theory and Modern Computations. Springer-Verlag New York, 1989, 247 pages.
Emil Artin, Algebra with Galois Theory. Notes by Albert A. Blank, 1947, Courant Lecture Notes in Mathematics 15, Courant Institute of Mathematical Sciences, 2007, 126 pages.
Emil Artin, Algebraic Numbers and Algebraic Functions. AMS Chelsea Publishing, 2005, 349 pages.
Georges Gras, Class Field Theory: From Theory to Practice, Second printing. Springer monographs in mathematics, Springer-Verlag Berlin Heidelberg, 2005, 491 + 18 pages.
Frits Beukers, A note on the irrationality of ζ(2) and ζ(3). Bulletin of the London Mathematical Society, vol. 11, n°3, octobre 1979, pages 268–272, doi:10.1112/blms/11.3.268.
G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers. Oxford University Press, 2008, 832 pages.
Helmut Koch, Galois Theory of p-Extensions, Second printing. Springer monographs in mathematics, Springer-Verlag Berlin Heidelberg, 2010, 190 pages.
Hendrik W. Lenstra, Solving the Pell equation, dans J. P. Buhler & P. Stevenhagen, Algorithmic number theory, pages 1–23, Mathematical Sciences Research Institute Publications, Cambridge University Press, 1998.
Ian Stewart & David Tall, Algebraic Number Theory. Prentice Hall, 1984, 356 pages.
Janusz, Gerald J., Algebraic Number Fields, Second edition. American Mathematical Society, 1996, 528 pages.
Jürgen Neukirch, Algebraic Number Theory. Grundlehren der Mathematischen Wissenschaften 322, Springer-Verlag Berlin Heidelberg, 1999, 571 pages.
Jürgen Neukirch, Class Field Theory. Grundlehren der Mathematischen Wissenschaften 280, Springer-Verlag Berlin Heidelberg, 1986, 140 pages.
Jürgen Neukirch, Alexander Schmidt, Kay Wingberg, Cohomology of Number Fields, Second printing. Grundlehren der Mathematischen Wissenschaften 323, Springer-Verlag Berlin Heidelberg, 2013, 826 pages.
Kenneth Ireland, Michael Rosen, A Classical Introduction to Modern Number Theory. Graduate texts in mathematics 84, Springer-Verlag New York, 1982, 341 pages.
Lawrence Clinton Washington, Introduction to Cyclotomic Fields, Second edition. Graduate texts in mathematics 83, Springer-Verlag New York, 1982, 487 pages.
M. Couchouron, Développement d’un réel en fractions continues, complément de cours de la préparation à l’agrégation de mathématiques de l’université de Rennes 1, mai 2003.
Pierre Colmez, Éléments d’analyse et d’algèbre (et de théorie des nombres). Dunod, 2001, 264 pages.
Pierre Samuel, Théorie algébrique des nombres. Hermann, 2003, 368 pages.
Serge Lang, Algebra. Addison-Wesley, 2002, 814 pages.
Serge Lang, Algebraic Number Theory. Addison-Wesley series in mathematics 4201, Addison-Wesley Publishing Company, Reading, Massachusetts, 1970, 354 pages.
S. Saks & A. Zygmund, Fonctions analytiques. Springer, 1969, 304 pages.
David Archibald Cox, Primes of the Form x² + ny²: Fermat, Class Field Theory, and Complex Multiplication, Second edition. Pure and Applied Mathematics, Wiley, 2013, 356 pages.
Franz Lemmermeyer, Reciprocity Laws: From Euler to Eisenstein. Springer monographs in mathematics, Springer-Verlag Berlin Heidelberg, 2000, 487 pages.
Don Zagier, Newman's Short Proof of the Prime Number Theorem, The American Mathematical Monthly, vol. 104, n°8, octobre 1997, pages 705–708, doi:10.2307/2975232.
Henri Cohen, A Course in Computational Algebraic Number Theory. Fourth printing, Graduate texts in mathematics 138, Springer-Verlag Berlin Heidelberg, 2000, 551 pages.
Henri Cohen, Advanced Topics in Computational Number Theory. Graduate texts in mathematics 193, Springer-Verlag New York, 2000, 578 pages.
I. R. Shafarevich, Extensions with Prescribed Ramification Points. Publ. Math., Inst. Hautes Etudes Sci. 18 (1964), 71–95. English transl. by J. W. S. Cassels in Amer. Math. Soc. Transl., II. Ser., 59 (1966), 128–149.
J.W.S. Cassels, A. Fröhlich, Editors, Algebraic Number Theory. Proceedings of an instructional conference organized by the London Mathematical Society, Academic Press, 1967, 366 pages.