Class Field Theory

Abstract

In this thesis, we state and sketch the proofs of main theorems of class field theory. There are many approaches to studying class field theory. We take the cohomological approach to prove the main results for the local case and then using these results establish analogous results for global fields. We briefly discuss John Tate’s seminal thesis on meromorphic analytic continuation of L-functions and their functional equations. No claim is made about originality of content and exposition.