"The book is outstanding and admirable in many respects. ... is necessary reading for all kinds of readers from undergraduate students to top authorities in the field." Journal of Symbolic Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and their applications of Kolmogorov complexity. the book presents a thorough treatment of the subject with a wide range of illsutrative applications. Such applications include the randomeness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computationla learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. the book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and himnts to solutions of problems. In this new edition the authors have added new material on circuit theory, distributed algorithms, data compression, and other topics.