Dissipative Quantum Chaos and Decoherence provides an overview of the state of the art of research in this exciting field. The main emphasis is on the development of a semiclassical formalism that allows one to incorporate the effect of dissipation and decoherence in a precise, yet tractable way into the quantum mechanics of classically chaotic systems. The formalism is employed to reveal how the spectrum of the quantum mechanical propagator of a density matrix is determined by the spectrum of the corresponding classical propagator of phase space density. Simple quantum--classical...