"Chaitin has produced very deep results, with tremendous impact on mathematics, computer technology and philosopy (and, in particular, on GIT). His new book is another piece of jewellery in his (already) large gallery." Cristian Calude Bulletin (EATCS) "The book under review is an extraordinary mathematical monograph." M I Dekhtyar Mathematical Reviews "... the reviewer found the book most stimulating and highly recommends it." A A Mullin Mathematics Abstracts