This is a project in abstract algebra. It deals mainly with homological methods in non-commutative algebra, in particular related to representation theory, derived categories and A-infinity algebras. Below the main topics are listed:
1. Infinite length mo dules and (co)tilting.
2. Varieties of modules.
3. Finitely generated cotilting modules.
4. Tilting and derived categories.
5. The theory of A-infinite algebras and categories.
6. Examples of A-infinite algebras.
7. Applications of A-infinite algebras.