This book introduces the quantum mechanics of classically chaotic systems, or quantum chaos for short. The author's philosophy has been to keep the discussion simple and to illustrate theory, wherever possible, with experimental or numerical examples. The microwave billiard experiments, initiated by the author and his group, play a major role in this respect. Topics covered include the various types of billiard experiment, random matrix theory, systems with periodic time dependences, the analogy between the dynamics of a one-dimensional gas with a repulsive interaction and spectral level dynamics, where an external parameter takes the role of time, scattering theory distributions and fluctuation, properties of scattering matrix elements, semiclassical quantum mechanics, periodic orbit theory, and the Gutzwiller trace formula. This book will be of great value to anyone working in quantum chaos.

"At present this seems to be the best textbook on quantum chaos. It strikes the right balance between the presentation of theory and experiment." Pageoph

"Reading Stöckmann's monograph gives a good picture of the most important results that the idea of quantum chaos has generated in the last three decades." American Journal of Physics

"A remarkable work, reflecting the growth and excitement of the field and containing something for almost everyone interested in chaos theory and experiment...The style and clarity of writing are both excellent...the book is valuable and will fast become a 'must have' for those with an interest in quantum chaos." Physics Today