Since the 1950s, many new ideas and tools from algebra, and algebraic and geometric topology, have been applied to study the structure of high-dimensional differential and topological manifolds, and so today it can be difficult for beginners to delve through the literature. This volume is a helpful guide to the basic concepts and results of topology of manifolds -- including the h- and s-cobordism theorems, topological invariance of rational Pontryagin classes, surgery theory, and algebraic K-theory.