This thoroughly revised 5th edition of Zeh's classic text investigates irreversible phenomena and their foundation in classical, quantum and cosmological settings. It includes new sections on the meaning of probabilities in a cosmological context, irreversible aspects of quantum computers, and various consequences of the expansion of the Universe. Many other sections have been rewritten. In particular, the book contains an analysis of the physical concept of time, a detailed treatment of radiation damping as well as extended sections on 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 will find in this book a magnificent survey and a concise, technically sophisticated, up-to-date discussion which shows fine sensitivity to crucial conceptual subtleties. "The discussion is lucid and intuitive without glossing over the important details." Max Tegmark, MIT.