This modern approach to homological algebra by two leading writers in the field is based on the systematic use of the language and ideas of derived categories and derived functors. It describes relations with standard cohomology theory and provides complete proofs. Coverage also presents basic concepts and results of homotopical algebra. This second edition contains numerous corrections.
However, be prepared to go through dozens of errors.
No other book gets you to the heart of homological algebra as fast as this one.
From a comparison point of view, this book is different from a more algebraic inclined one such as Wiebel's or Cartan&Eilenberg. Those are written for and by algebraists/topologists.
This book is written for the mathematician or mathematical physicist in mind.