This book provides a comprehensive and up-to-date introduction to Hodge theory--one of the central and most vibrant areas of contemporary mathematics--from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures...