The collision and non-linear interaction of plane waves in Einstein's general theory of relativity has received considerable attention in recent years. Initially, it was widely thought that such collisions inevitable produce curvature singularities. More recently, however, a surprisingly rich structure of such space-times has been discovered. This volume presents a unified and comprehensive survey to the current research in this topic which will be suitable for graduate students and research workers whose research lies in general relativity. The first eight chapters present the background to the subject, introduce the field equations, and include a discussion of some qualitative aspects of their solution. A detailed account is included of the Kahn-Penrose solution since it exhibits the general character of most colliding plane wave solutions. The latter half of the book is devoted to a catalogue of further exact solutions describing the collision of both gravitational and electromagnetic plane waves. This includes a discussion of the significance of known solutions and a summary of topics of current research interest. As a result, the book will serve both as an invaluable research reference and also as the means to teach and study this active area of research in general relativity.