I will review the classic paper by Atiyah and Bott titled "The Moment Map and Equivariant Cohomology". The motivational statement of that paper is that if f is a function on a symplectic manifold M whose hamiltonian flow generates a circle action, the integral of $e^&ob;if&cb;$ localizes to a certain integral over the critical locus of f. First, I will briefly tell you why I'm personally interested in this theorem, (it tells you stuff about complex Chern Simons theory,) then I will talk about how to prove it. The proof will be easy once we learn about equivariant cohomology, and how to do equivariant cohomology in a de Rahm way.