Class Field Theory and Introduction to Iwasawa Theory

Abstract

The central objective of this thesis is to state and prove the main theorems of local and global class field theory. We first give a brief overview of basic algebraic number theory followed by group cohomology. Then, we prove the results of local class field theory using cohomology and then prove the global results using the local ones via ideles. Our treatment of Iwasawa theory discusses basic facts and just touches the surface of a very deep subject. We do not claim the originality of contents and exposition.