The book focuses on a Lisp formalism for examining fundamental theories, notions, and findings regarding program-size complexity and random sequences.

Numerous exercises are included in the book, ranging from the "mathematical equivalent of finger warm-ups for pianists" to extensive programming tasks, from open inquiries to queries the author is unable to even conceive of. Strongly advised for anyone looking to learn algorithmic information theory through programming.

The technical foundation of Chaitin's theory of program-size complexity is presented in this crucial companion volume to his best-selling works The Unknowable and The Limits of Mathematics. The focus of the two earlier volumes was on applications to meta-mathematics.

The main algorithms are presented using LISP, allowing computer users to interact with the author's proofs and ascertain for themselves how they operate. On the author's website, a Java applet LISP interpreter as well as the LISP code for this book are also accessible. "Greg Chaitin is the only person to have delved deeper and further into the depths of randomness and its use in mathematics. Everything he has seen is described in this book. Miss it not." Goedel: A Life of Logic is written by John Casti of the Santa Fe Institute.