| 1 | Course Introduction, Zariski Topology (PDF) |
| 2 | Affine Varieties (PDF) |
| 3 | Projective Varieties, Noether Normalization (PDF) |
| 4 | Grassmannians, Finite and Affine Morphisms (PDF) |
| 5 | More on Finite Morphisms and Irreducible Varieties (PDF) |
| 6 | Function Field, Dominant Maps (PDF) |
| 7 | Product of Varieties, Separatedness (PDF) |
| 8 | Product Topology, Complete Varieties (PDF) |
| 9 | Chow's Lemma, Blowups (PDF) |
| 10 | Sheaves, Invertible Sheaves on P1 (PDF) |
| 11 | Sheaf Functors and Quasi-coherent Sheaves (PDF) |
| 12 | Quasi-coherent and Coherent Sheaves (PDF) |
| 13 | Invertible Sheaves (PDF) |
| 14 | (Quasi)coherent Sheaves on Projective Spaces (PDF) |
| 15 | Divisors and the Picard Group (PDF) |
| 16 | Bezout's Theorem (PDF) |
| 17 | Abel-Jacobi Map, Elliptic Curves (PDF) |
| 18 | Kähler Differentials (PDF) |
| 19 | Smoothness, Canonical Bundles, the Adjunction Formula (PDF) |
| 20 | (Co)tangent Bundles of Grassmannians (PDF) |
| 21 | Riemann-Hurwitz Formula, Chevalley's Theorem (PDF) |
| 22 | Bertini's Theorem, Coherent Sheves on Curves (PDF) |
| 23 | Derived Functors, Existence of Sheaf Cohomology (PDF) |
| 24 | Birkhoff–Grothendieck, Riemann-Roch, Serre Duality (PDF) |
| 25 | Proof of Serre Duality (PDF) |
