A draft of “Derived Categories — a Textbook” by Amnon Yekutieli has appeared on the arXiv recently. Here is the abstract:
This is the first part of a book on derived categories. The purpose of the book is to provide solid foundations for the theory of derived categories, and to present several applications of this theory to algebra and algebraic geometry. The emphasis is on constructions and examples, rather than on axiomatics.
The second part of the book is expected to be finished in 2017.