Sheaves theory: sheaves and sheafification. Quasi-coherent sheaves. Locally free sheaves. Differentials. Line bundles on curves. The Riemann-Hurwitz formula. The Riemann-Roch theorem.

Cohomology of sheaves: Definitions. The long exact cohomology sequence. The Riemann-Roch theorem revisited. The cohomology of line bundles on projective spaces. Independence of the affine cover.

Intersection theory: Chow groups. Proper push-forward of cycles. Weil and Cartier divisors. Intersection with Cartier divisors.

Chern classes: Projective bundles. Segre and Chern classes of projective bundles. Properties of Chern classes. Hirzebruch-Riemann-Roch theorem.