In the first half of the talk, we shall go through the definitions of manifold, cobordism, h-cobordism, Morse functions and gradient-like flows, and demonstrate many of their properties. In the second half of the talk we shall give an outline of the proof. In the process, we shall prove lemmas about commutation and cancellation of critical points, and see the Whitney trick in action. Time permitting, we shall show how the h-cobordism theorem proves the topological Poincare conjecture in high dimensions.