This series of lectures will introduce some of the basic theory of mean curvature including the variational theory of the volume functional and its geometrical significance. We will summarize (without proof) the existence theory of minimizers and for min/max hypersurfaces. We will also discuss certain nonvariational existence theorems which are used for constructing MOTS (see Dan Pollack's lectures). We will discuss curvature estimates and compactness theorems for classes of hypersurfaces. Finally we will discuss some of the applications of the theory to positive mass theorems and existence of black holes. We will highlight open problems (of which there are many) whenever possible.