awesome-number-theory
A list of awesome number theory resources
Elementary Number Theory
Richard E. Borcherds - Introduction to number theory
Detailed and insightful introduction.
Michael Penn - Number Theory v2
Easy to digest and fast introduction.
Algebraic Number Theory
Jürgen Neukirch - Algebraic Number Theory
The most famous algebraic number theory textbook.
Daniel Marcus - Number Fields
A lot of exercises.
Jean-Pierre Serre - Local Fields
Concentrates on local theory. Towards local class field theory.
James Milne - Algebraic Number Theory
Easy to read. Include solutions to exercises.
Analytic Number Theory
Tom Apostol - Introduction to Analytic Number Theory
Introductory book. Towards a proof of Dirichlet's theorem on arithmetic progressions using Dirichlet $L$-functions.
Class Field Theory
James Milne - Class Field Theory
Includes proof of local/global class field theory.
David Cox - Primes of the form $x^2 + ny^2$ (Fermat, Class Field Theory, and Complex Multiplication)
Classicial approach rather than modern adelic approach. It is less formal, but provides motivation.
Jürgen Neukirch - Class Field Theory
Cohomology of finite fields. Relatively comprehensive.
Automorphic Forms and Representations
Daniel Bump - Automorphic Forms and Representations
Concentrates on $\mathrm{GL}_2$ theory over $\mathbb{Q}$.
Jan Bruinier et al. - 1-2-3 of Modular Forms
Great book on elliptic/Hilbert/Siegel modular forms with tons of applications.
Jayce Getz, Heekyoung Hahn - An Introduction to Automorphic Forms (with a view toward Trace Formulae)
Modern aspects of automorphic forms and representations, beyond $\mathrm{GL}_2$.
Last chapters are devoted to (simple, relative) trace formulae with related topics.
Neal Koblitz - Introduction to Elliptic Curves and Modular Forms
Towards the theory of half-integral weight modular forms, Shimura correspondence, Waldspurger's formula and Tunnell's theorem on congruent numbers.
Fred Diamond, Jerry Shurman - A First Course in Modular Forms
Goal of the book is to understand the statement of Wiles' modularity theorem.
Larry Rolen - Modular Forms: Theory and Applications
Lectures at Vanderbilt University. Covers various topics related to modular forms.
Arithmetic Geometry
Joseph Silverman - The Arithmetic of Elliptic Curves
The most famous introductory textbook on elliptic curves. A bit of applications on cryptography included.
Joseph Silverman - Advanced Topics in the Arithmetic of Elliptic Curves
Volume 2 of Silverman's book. Include various topics that are not in the volume 1: elliptic and modular functions, CM elliptic curves, Neron models, Tate's algorithm, etc.
Joseph Silverman, Marc Hindry - Diophantine Geometry
Towards the proof of Faltings' theorem.
James Milne - Elliptic Curves
Nicely written. Introductory textbook.
Galois Representations
Iwasawa Theory
Misc
Cornell et al. - Modular Forms and Fermat's Last Theorem
Series of articles explaning the details of the proof of Fermat's Last Theorem.
Keith Conrad's expository papers
Tons of notes on various topics. Especially there are many useful notes on number theory written explicitly.
Anthony Vasaturo - Fermat's Last Theorem
Ongoing youtube series that aims to explain the proof of FLT.
Connecticut Summer School in Number Theory
Provide nice lectures on various topics in number theory.
Arizona Winter School
Annual winter school held at University of Arizona. All the lecture notes, videos, and exercises for the previous schools can be found.
awesome-number-theory copied to clipboard
seewoo5
seewoo5