Mixed Motives and their Realization in Derived Categories

The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. This text describes the approach to motives via their well-defined realizations, including a review of several known cohomology theories. A new absolute cohomology is introduced and studied. The book assumes knowledge of the standard cohomological techniques in algebraic geometry as well as K-theory, and so the monograph is primarily intended for researchers. Advanced graduate students can use it as a guide to the literature.