It is classical that one can use Morse Theory on the free loop space to study the existence of closed geodesics on a Riemannian manifold. I will discuss certain invariants (ordinary and equivariant cohomology) of the free loop space that have been useful to show the existence of infinitely many closed geodesics. It turns out that the homology of the free loop space has a product called the Chas Sullivan product which makes the homology of the free loop space into a ring. This product (and its equivariant counterpart called the string bracket) provides an interesting way of attacking the problem of existence of infinitely many closed geodesics.