Mean curvature flow (MCF) is the negative gradient flow of area functional. Any closed (hyper)surface flows in the direction of steepest descent for area and becomes singular in finite time. MCF arises from the study of crystal/grain growth, image processing, and other scientific fields. It also has some potential applications in low-dimension topology.

In a series of lectures, we will give a brief introduction to MCF and discuss how to analyze the asymptotic behaviors of the flow near singularities, in which Huisken's monotonicity formula and a notion of entropy introduced by Colding and Minicozzi play key roles.