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Preface 1. Basics of commutative algebra 2. Projective space and graded objects 3. Free resolutions and regular sequences 4. Gröbner bases 5. Combinatorics and topology 6. Functors: localization, hom, and tensor 7. Geometry of points 8. Homological algebra, derived functors 9. Curves, sheaves and cohomology 10. Projective dimension A. Abstract algebra primer B. Complex analysis primer Bibliography.