1. Algebraic functions
2. Riemann surfaces
3. The sheaf of germs of holomorphic functions
4. The Riemann surface of an algebraic function
5. Sheaves
6. Vector bundles, line bundles and divisors
7. Finiteness theorems
8. The Dolbeault isomorphism
9. Weyl's lemma and the Serre duality theorem
10. The Riemann-Roch theorem and some applications
11. Further properties of compact Riemann surfaces
12. Hyperelliptic curves and the canonical map
13. Some geometry of curves in projective space
14. Bilinear relations
15. The Jacobian and Abel's theorem
16. The Riemann theta function
17. The theta divisor
18. Torelli's theorem
19. Riemann's theorem on the singularities of θ
References
