This ongoing bestseller, now in its third edition, is considered the standard reference on Kolmogorov complexity, a modern theory of information that is concerned with information in individual objects. New key features and topics in the 3rd edition: * New results on randomness * Kolmogorov's structure function, model selection, and MDL * Incompressibility method: counting unlabeled graphs, Shellsort, communication complexity * Derandomization * Kolmogorov complexity versus Shannon information, rate distortion, lossy compression, denoising * Theoretical results on information distance * The similarity metric with applications to genomics, phylogeny, clustering, classification, semantic meaning, question-answer systems *Quantum Kolmogorov complexity Written by two experts in the field, this book is ideal for advanced undergraduate students, graduate students, and researchers in all fields of science. It is self-contained: it contains the basic requirements from mathematics, probability theory, statistics, information theory, and computer science. Included are history, theory, new developments, a wide range of applications, numerous (new) problem sets, comments, source references, and hints to solutions of problems. This is the only comprehensive treatment of the central ideas of Kolmogorov complexity and their applications. ``Li and Vitányi have provided an ideal book for the exploration of a deep, beautiful and important part of computer science.'' -- Juris Hartmanis, Turing Award Winner 1993, Cornell University, Ithaca, NY. ``The book is likely to remain the standard treatment of Kolmogorov complexity for a long time.'' -- Jorma J. Rissanen, IBM Research, California. ``The book of Li and Vitányi is unexcelled.'' -- Ray J. Solomonoff, Oxbridge Research, Cambridge, Massachusetts "The book is outstanding...the authors did their job unbelievably well...necessary reading for all kinds of readers from undergraduate students to top authorities in the field." -- Vladimir A. Uspensky and Alexander K. Shen, Journal of Symbolic Logic [Review] ``Careful and clear introduction to a subtle and deep field.'' --David G. Stork, Ricoh Innovations, California, Amazon [Review] ``THE book on Kolmogorov Complexity.'' --Lance Fortnow, University of Chicago, IL, Amazon [Review].