It is a well-known fact that if we have a Lie group G acting on a smooth manifold M freely and properly, then the quotient is also a smooth manifold. In this talk, we will describe a modification of this process in the case M is a symplectic manifold and the G-action is Hamiltonian which will allow us to find a quotient with a canonical symplectic form. More concretely, we will discuss moment maps for Hamiltonian actions and the Marsden-Weinstein-Meyer reduction theorem. If time permits, we will describe how this relates to algebraic (GIT) quotients (Kempf-Ness theorem). Speaker(s): Reebhu Bhattacharyya (University of Michigan)