The study of the spectra and related characteristics of random and almost periodic operators of various types (Schrödinger, continuous, discrete and more general) is a lively and fascinating field of research lying at the intersection of mathematical physics, spectral theory of operators and probability theory. A widespread interest in the domain and a vast amount of mathematical activity have led to many remarkable new results and viewpoints yielding insight even into traditional questions. This book by two of the leading researchers having contributed to this field is the first systematic treatment of the fundamental problems and the large body of mathematical results known, and thus fills the gap in the reference literature. Not content to highlight the important ideas and recently developed concepts and methods, it also provides a large number of exercises illustrating these, to guide the reader towards improvements and generalizations. This long-awaited book is a welcome addition to the literature both for specialists in the field and for graduate students moving into research, as well as for all interested in the major problems of mathematical physics today.