The curve shortening flow for convex curves ; The short time existence and the evolution equation of curvatures ; Contraction of convex hypersurfaces ; Monotonicity and self-similar solutions ; Evolution of embedded curves or surfaces (I) ; Evolution of embedded curves and surfaces (II) ; Evolution of embedded curves and surfaces (III) ; Convexity estimates for mean convex surfaces ; Li-Yau estimates and type II singularities ; The mean curvature flow in Riemannian manifolds ; Contracting convex hypersurfaces in Riemannian manifolds ; Definition of center of mass for isolated gravitating systems