This book has been thoroughly revised to include important new results. At the same time it retains the features that make it a classic text on irreversibility, and one which clearly distinguishes the latter from those time asymmetries which may be compensated for by other asymmetries. The book investigates irreversible phenomena in classical, quantum and cosmological settings. In particular, this fourth edition contains a revised treatment of radiation damping as well as extended sections on dynamical maps, quantum entanglement and decoherence, arrows of time hidden in various interpretations of quantum theory, and the emergence of time in quantum gravity. Both physicists and philosophers of science who reviewed earlier editions considered this book a magnificent survey, a concise, technically sophisticated, up-to-date discussion of the subject, showing showing fine sensitivity to crucial conceptual subtleties.