Boundary-layer separation from a rigid body surface is one of the fundamental problems in classical and modern fluid dynamics. This book, a revised translation of the classic Russian edition, takes state-of-the-art triple-deck boundary layer theory to a broad new audience. The authors present this important theory in a unique, systematic account that covers numerical methods for solving the equations of interaction theory and the theory of unsteady separation. The book will serve as a useful introduction to the theory, drawing attention to the new possibilities that application of the asymptotic approach provides. It will be an essential reference for mathematicians, physicists, and engineers.