Number Theory II: Class Field Theory
An MIT OpenCourseWare continuation of Number Theory I, covering advanced algebraic number theory. The course opens with the quadratic case of class field theory via Hilbert symbols to build intuition before moving to the general theory. Topics include Galois cohomology, proofs of the main theorems of class field theory, modular and automorphic forms, Galois representations, and quadratic forms. Materials include lecture notes and problem sets from MIT's graduate mathematics curriculum, published under a Creative Commons license with no cost to access. Intended for students who have already completed a first course in number theory, it assumes comfort with algebraic structures like fields, rings, and Galois theory. There is no instructor interaction or certificate, but the full set of course materials is freely downloadable for self-study.