Syllabus
1. C-filtrations, Hill Lemma and its consequences.
2. Approximations of modules and complete cotorsion pairs.
3. Modules of bounded homological dimensions.
4. Purity and deconstruction of modules.
5. Minimal approximations, flat covers, and the Enochs Problem.
6. Tilting modules and approximations.
7. Classes of finite type.
8. Finitistic dimension conjectures.
Annotation
An introduction to the theory of envelopes and covers of modules. Complete cotorsion pairs. The proof of the Flat Cover
Conjecture. Tilting approximations. Connections to the Finitistic Dimension Conjectures for algebras. Solution to the Baer
Problem.