Vladimir Retakh
This will be an introduction to Homological Algebra. Homological Algebra is a tool used in many branches of mathematics, especially in Algebra, Topology and Algebraic Geometry. The first part of the course will cover Chain Complexes, Projective and Injective Modules, Derived Functors, Ext and Tor. In addition, some basic notions of Category Theory will be presented: adjoint functors, abelian categories, natural transformations, limits and colimits. The second part of the course will study Spectral Sequences, and apply this to several topics such as Homology of Groups and Lie Algebras.
An introduction to homological algebra, by C. Weibel, Cambridge University Press
Math 551, 552