This will be an introduction to the subject of 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. Which topics we cover will be determined by the interests of the students in the class.
Notes from class
An introduction to homological algebra, by C. Weibel, Cambridge University Press, paperback edition (1995)