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1. Homological preliminaries;
2. Adic topologies and completions;
3. Injective envelopes and minimal injective resolutions;
4. Local cohomology and koszul complexes;
5. (Pre-) Regular sequences and depth;
6. Exactness of complexes and linear equations over rings;
7. Comparing homological invariants;
8. Dimensions;
9. Cohen-Macauley modules and regular rings;
10. Gorenstein rings, local duality, and the direct summand conjecture;
11. Frobenius and big Cohen-Macauley modules;
12. Big Cohen-Macaulay modules in equal charecteristic 0;
13. Uses of big Cohen-Maculay Modules.
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