Provides an introduction to Hodge theory - one of the central and most vibrant areas of contemporary mathematics - from leading specialists on the subject. This book includes topics that range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps.
"Between 14 June and 2 July 2010, the Summer School on Hodge Theory and Related Topics and a related conference were hosted by the ICTP in Trieste, Italy" --Preface (page xv).
"Charles and Schnell's chapter beautifully surveys the theory of absolute Hodge classes, giving in particular a complete proof of Deligne's theorem on absolute Hodge classes on abelian varieties. . . . A welcome addition to the literature and should be useful to both graduate students and researchers working in Hodge theory."
---Dan Petersen, MathSciNet
