"Methods of Homological Algebra" is a textbook that deals with modern homological algebra. It provides a comprehensive introduction to the language and concepts of derived categories and derived functors. The authors, who are leading experts in the field, explain the connections to standard cohomology theory, including sheaf cohomology and spectral sequences. The book is aimed at professionals and students who wish to gain a deeper understanding of modern approaches in homological algebra. The second edition includes numerous corrections that enhance the clarity and accuracy of the content. With complete proofs and a systematic approach, this work is a valuable reference for anyone engaged with the theoretical foundations and applications of homological algebra.