Lev Borisov
This will be an introduction to Homological Algebra. Homological Algebra is used in various 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. 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 their applications depending of the interests of the students in the class.
An introduction to homological algebra, by C. Weibel, Cambridge University Press, paperback edition
First semester of graduate algebra.