We will start by defining a general class of geometric flows in which there is local existence. We will then focus on specific flows to discuss global behavior and applications. This will serve as an overview meant to motivate the utility of these geometric flows.

This will include (with time-permitting) the following topics:

- Mean curvature flow and the topological characterization of 2-convex closed hypersurfaces in Euclidean space.
- Gauss curvature flow as a physical model for stone tumbling.
- Inverse mean curvature flow and the Riemannian Penrose inequality in general relativity.

Some knowledge of Riemannian geometry will be assumed.