
Basic level:
 A. Caldararu, Derived categories of sheaves: a skimming, available
at http://www.math.wisc.edu/~andreic/publications/lnPoland.pdf
 D. Milicic, Notes for the Derived Categories class, available at
http://www.math.utah.edu/~milicic/dercat.pdf
 S. Gelfand and Yu. Manin, Methods of Homological Algebra, Springer
Monographs in Mathematics.
 C. Weibel, An Introduction to Homological Algebra (Chapter 10),
Cambridge University Press.
 Richard Thomas, "Derived categories for the working mathematician," math/0001045
Advanced level:
 T. Bridgeland, Derived categories of coherent sheaves, available at
http://arxiv.org/abs/math.AG/0602129
 D. Huybrechts, FourierMukai transforms in algebraic geometry.
Oxford Mathematical Monographs.

M. Kontsevich, Homological Algebra of Mirror Symmetry, available at
http://arxiv.org/abs/alggeom/9411018
