This book is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more). In the 20 years since, the importance of Bloch's lectures has t diminished. A lucky group of people working in the above areas had the good fortune to possess a copy of old typewritten tes of these lectures. Now everyone can have their own copy of this classic work. Titles in this series are co-published with the Centre de Recherches Mathematiques.