Time Reversal and Unitary Symmetries -- Level Repulsion -- Random-Matrix Theory -- Level Clustering -- Level Dynamics -- Quantum Localization -- Dissipative Systems -- Classical Hamiltonian Chaos -- Semiclassical Roles for Classical Orbits -- Superanalysis for Random-Matrix Theory.

This by now classic text provides an excellent introduction and survey to the continuously expanding field of quantum chaos . The topics treated include a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria to distinguish regular and irregular motion, antiunitary symmetries (generalized time reversal), random matrix theory and a thorough account of the quantum mechanics of dissipative systems. Each chapter is accompanied by a selection of problems which will help the newcomer to test and deepen his/her understanding and to acquire an active command of the methods presented. In addition to a significant number of smaller revisions and chapter updates, the third edition thoroughly expands on the understanding of universal spectral fluctuations, and – to subsequently make the presentation of all semi-classical developments self-contained - a new chapter on classical Hamiltonian chaos has been inserted. From the reviews of the 2nd edition: In summary, this is definitely an essential reference book for the specialist. It will also ably serve someone entering the field for the first time who needs to learn the theoretical state of the art in detail." (G. Summy ,University of Oxford, Contemporary Physics 2002, vol. 43, p 232)