*Title:*
**Introduction
to Derived Categories **

*Author:
*Amnon
Yekutieli

*Publication
status:*
appeared
in: ``Commutative Algebra and Noncommutative Algebraic Geometry, I'',
MSRI Publications **67**,
2015.

*Abstract*:
Derived categories were invented by Grothendieck and Verdier around
1960, not very long after the “old” homological algebra (of
derived functors between abelian categories) was established. This
“new” homological algebra, of derived categories and derived
functors between them, provides a significantly richer and more
flexible machinery than the “old” homological algebra. For
instance, the important concepts of dualizing complex and tilting
complex do not exist in the “old” homological algebra.

This paper is an edited version of the notes for a two-lecture minicourse given at MSRI in January 2013. Sections 1-5 are about the general theory of derived categories, and the material is taken from my manuscript “A Course on Derived Categories” (available online). Sections 6-9 are on more specialized topics, leaning towards noncommutative algebraic geometry.

updated 11 Sep 2016