This two week summer graduate school is a collaboration between MSRI and the IACM-FORTH Institute in Crete. The purpose of the school is to introduce graduate students to some of the most important geometric evolution equations. This is an area of geometric analysis that lies at the interface of differential geometry and partial differential equations. The lectures will begin with an introduction to nonlinear diffusion equations and continue with classical results on the Ricci Flow, the Mean curvature flow and other fully non-linear extrinsic flows. The lectures will conclude with recent developments related to the study of singularities and ancient solutions. There will be ample time for problem and research discussions between participants of all levels.Geometric Flows, Summer Graduate School 2020 was originally scheduled for June 15th – June 26th, Heraklion, Greece. Postponed due to the coronavirus crisis.