Abstract:
The goal of the project is to study Class Field Theory. Class Field Theory studies the
abelian extensions of local elds and global elds. There are di erent approaches for this
and we focus on the cohomological approach envisaged by Hochschild and Nakayama. We
give an exposition on how to prove certain theorems in Elementary Number Theory, using
Class Field Theory. Also, we discuss the solution to a long-standing problem.
