This book contains in easily accessible form all the main ideas of the creator and principal architect of algorithmic information theory. This expanded second edition has added thirteen abstracts, a 1988 Scientific American Article, a transcript of a EUROPALIA 89 lecture, an essay on biology, and an extensive bibliography. Its new larger format makes it easier to read. Chaitin's ideas are a fundamental extension of those of Gödel and Turning and have exploded some basic assumptions of mathematics and thrown new light on the scientific method, epistemology, probability theory, and of course computer science and information theory.