This book deals with the statistical mechanics and dynamics of open quantum systems moving irreversibly under the influence of a dissipative environment. The basic concepts and methods are described on the basis of a microscopic description with emphasis on the functional integral approach. The general theory for the time evolution of the density matrix of the damped system is developed. Many of the sophisticated ideas in the field are explained with simple models. The discussion includes, among others, the interplay between thermal and quantum fluctuations, quantum statistical decay, macroscopic quantum tunneling and quantum coherence.