This volume of the Encyclopaedia presents a modern approachto homological algebra, which is based on the systematic useof the terminology and ideas of derived categories andderived functors. The book contains applications ofhomological algebra to the theory of sheaves on topologicalspaces, to Hodge theory, and to the theory of sheaves ontopological spaces, to Hodge theory, and to the theory ofmodules over rings of algebraic differential operators(algebraic D-modules). The authors Gelfand and Manin explainall the main ideas of the theory of derived categories. Bothauthors are well-known researchers and the second, Manin, isfamousfor his work in algebraic geometry and mathematicalphysics. The book isan excellent reference for graduate students andresearchers in mathematics and also for physicists who usemethods from algebraic geomtry and algebraictopology.