This volume is the only monograph covering the exciting and dazzling recent developments in quantum cosmology, including the theory of the multiverse and eternal inflation pioneered by A Vilenkin, A Linde, S W Hawking, and others. Written by a leading expert in the field known for his depth and clarity of presentation, the volume presents an overview of 20 years of development of the theory of eternal inflation as well as a comprehensive, research-level introduction into the current methods and problems. This volume is invaluable for researchers as a definitive reference in the rapidly developing field. Written in a self-contained manner with detailed mathematical derivations of the results, graduate students will also find it a readable and useful textbook for self-study.