Ian Coley
Homological algebra is an essential tool in algebraic geometry and algebraic topology and find use in representation theory, Lie theory, and much more. Roughly, it is a first step in applying some category theory to questions of concrete interest. Main topics: chain complexes, abelian and triangulated categories, derived functors, (co)homology. Actual computations will be emphasized!
An introduction to Homological Algebra, Weibel [other resources TBD]
451-2 (or permission)