The book provides all the tools needed for a productive use of the theory. Written by leading experts in the field, the book is both a fascinating introduction as well as a comprehensive reference for experts. The authors are careful to place the development of the theory in its historical context, give a face to the main players in the field and explore frictions with other lines of thought. But the main storyline is the mathematical world of Kolmogorov complexity. Neccessary background knowledge is provided, most proofs are given and the open problems are presented. Most chapters are more or less self sufficient, making it possible to skip those that are of less relevance to you. In the later chapters much thought is given to the different fields of application. A third edition is in the making which will include recent advances. But since the authors make new discoveries available on the web, the present edition will continue for a long time to hold a prominent place in the book shelves of many computer scientist.