Basic level:

1. A. Caldararu, Derived categories of sheaves: a skimming, available at http://www.math.wisc.edu/~andreic/publications/lnPoland.pdf


2. D. Milicic, Notes for the Derived Categories class, available at http://www.math.utah.edu/~milicic/dercat.pdf


3. S. Gelfand and Yu. Manin, Methods of Homological Algebra, Springer Monographs in Mathematics.


4. C. Weibel, An Introduction to Homological Algebra (Chapter 10), Cambridge University Press.


5. Richard Thomas, "Derived categories for the working mathematician," math/0001045

Advanced level:

1. T. Bridgeland, Derived categories of coherent sheaves, available at http://arxiv.org/abs/math.AG/0602129


2. D. Huybrechts, Fourier-Mukai transforms in algebraic geometry. Oxford Mathematical Monographs.


3. M. Kontsevich, Homological Algebra of Mirror Symmetry, available at http://arxiv.org/abs/alg-geom/9411018