This textbook on commutative algebra presents basic results necessary for elementary algebraic geometry and introduces basic homological algebra and homological methods in commutative algebra. Its lecture-notes style will help readers with some mathematical maturity to study it on their own. Motivations are given at a number of places, examples follow every definition and exercises are given at the end of each section.
Contents: Preface. 1. Modules. 2. Localisation. 3. Noetherian rings. 4. Integral extensions. 5. Dedekind domains. 6. Completions. 7. Homology. 8. Dimension. 9. Regular local rings. 10. Some conjectures.
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