A brief overview of Hamiltonian Floer homology

I will first introduce Morse homology for finite dimensional manifolds.  Then, I will explain how the Arnold conjecture for Hamiltonian periodic orbits naturally leads to an infinite dimensional Morse homology theory on the loop space, called Floer homology.  Time permitting,  we will see how a ring structure on this homology is related to Gromov-Witten invariants and quantum cohomology.