This book provides a comprehensive and up-to-date introduction to Hodge theoryone of the central and most vibrant areas of contemporary mathematicsfrom 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. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesnt require a deep background. At the same time, the book presents some topics at the forefront of current research.The book is divided between introductory and advanced lectures. The introductory lectures address Khler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendiecks algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Delignes theorem on absolute Hodge cycles), and variation of mixed Hodge structures.The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, Franois Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, L Dng Trng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.