This course explores homological theory of commutative rings and aims to cover the following topics: 1. Commutative rings and modules 2. Localization and Spec of a ring 3. Completions and Artin Rees Lemma 4. Graded rings, Hilbert function and the Samuel function 5. System of parameters and multiplicity 6. Regular sequences and depth 7. Koszul Complexes 8. Cohen-Macaulay rings and modules 9. Gorenstien rings 10. Regular rings