There have been remarkably few systematic expositions of the theory of
derived categories since its inception in the work of Grothendieck and
Verdier in the 1960s. This book is the first in-depth treatment of this
important component of homological algebra. It carefully explains the
foundations in detail before moving on to key applications in
commutative and noncommutative algebra, many otherwise unavailable
outside of research articles. These include commutative and
noncommutative dualizing complexes, perfect DG modules, and tilting DG
bimodules. Written with graduate students in mind, the emphasis here is
on explicit constructions (with many examples and exercises) as opposed
to axiomatics, with the goal of demystifying this difficult subject.
Beyond serving as a thorough introduction for students, it will serve as
an important reference for researchers in algebra, geometry and
mathematical physics.