Here I list some books on number theory, algebraic geometry, arithmetic geometry etc. I will try to include only the books that I have read (entirely, or partially) myself.


Number Theory:

  1. J. W. S. Cassels, A. Fröhlich, Algebraic Number Theory.
  2. G. J. Janusz, Algebraic Number Fields.
  3. S. Lang, Algebraic Number Theory.
  4. D. A. Marcus, Number Fields.
  5. J. Neukirch, Algebraic Number Theory.
  6. P. Samuel, Algebraic Theory of Numbers.
  7. J. Neukirch, A. Schmidt, Class Field Theory – Bonn Lectures.
  8. K. Kato, N. Kurokawa, T. Saito. Number Theory 1: Fermat’s Dream.
  9. K. Kato, N. Kurokawa, T. Saito. Number Theory 2: Introduction to Class Field Theory.
  10. N. Kurokawa, M. Kurihara, T. Saito. Number Theory 3: Iwasawa Theory and Modular Forms.

Algebraic Geometry:

  1. R. Hartshorne, Algebraic Geometry.
  2. Q. Liu, Algebraic Geometry and Arithmetic Curves.
  3. U. Görtz and T. Wedhorn, Algebraic Geometry I, Schemes.
  4. K. Ueno, Algebraic Geometry 1: From Algebraic Varieties to Schemes.
  5. K. Ueno, Algebraic Geometry 2: Sheaves and Cohomology.
  6. K. Ueno, Algebraic Geometry 3: Further Study of Schemes.
  7. W. Waterhouse, Introduction to Affine Group Schemes.

Elliptic Curves, Abelian Varieties & Co.:

  1. J. Silverman, The Arithmetic of Elliptic Curves.
  2. J. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves.
  3. J. Silverman, J. Tate, Rational Points of Elliptic Curves.
  4. G. van der Geer, B. Moonen, Abelian Varieties.
  5. D. Mumford, Abelian Varieties.
  6. J. Milne, Abelian Varieties.
  7. F. Diamond, J. Shurman, A First Course in Modular Forms.
  8. J. Milne, Introduction to Shimura Varieties.

Specialized and Advanced Topics:

  1. G. Tamme, Introduction to Étale Cohomology.
  2. E. Freitag, R. Kiehl, Étale Cohomology And The Weil Conjecture.
  3. J. Milne, Étale Cohomology.
  4. S. Kudla, E. Kowalski, E. De Shalit, D. Gaitsgory, J. Cogdell, D. Bump, An Introduction to The Langlands Program.
  5. C. J. Bushnell, G. Henniart, The Local Langlands Conjecture For GL(2).
  6. G. Cornell, J. H. Silverman, Arithmetic Geometry.
  7.  B. Conrad, K. Rubin, Arithmetic Algebraic Geometry.
  8. G. Cornell, J. H. Silverman, G. Stevens, Modular Forms and Fermat’s Last Theorem.
  9. T. Saito. Fermat’s Last Theorem: Basic Tools.
  10. T. Saito. Fermat’s Last Theorem: The Proof.
  11. C.-L. Chai, G. Faltings, Degeneration of Abelian Varieties.
  12. S. Bosch, W. Lütkebohmert, M. Raynaud, Néron Models.
  13. J. Fresnel, M. van der Put, Rigid Analytic Geometry and its Applications.
  14. S. Bosch, Lectures on Formal and Rigid Geometry.
  15. A. Borel, W. Casselman, Automorphic Forms, Representations, and L-Functions I & II.
  16. M. Harris, R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties.