This is comprehensive basic monograph on mixed Hodge structures.
Building up from basic Hodge theory the book explains Delingne's mixed
Hodge theory in a detailed fashion. Then both Hain's and Morgan's
approaches to mixed Hodge theory related to homotopy theory are
sketched. Next comes the relative theory, and then the all encompassing
theory of mixed Hodge modules. The book is interlaced with chapters
containing applications. Three large appendices complete the book.