Vector bundles on compact Riemann surfaces

1. Cohomology of vector bundles and the duality theorem. 2. Divisors, line bundles and the Riemann-Roch theorem. 3. Projective embedding of a compact Riemann surface. 4. Genus and first Betti number. 5. Chern class and degree. 6. The Jacobian. 7. Line bundles and characters. 8. Poincare bundle. 9. The Picard manifold of a compact Kaehler manifold. 10. Vector bundles on a compact Riemann surface. 11. The Riemann-Roch theorem for vector bundles. 12. Indecomposable bundles and the Krull-Remak-Schmidt theorem. 13. Weil's theorem; unitary bundles. Appendix: Factors of automorphy. (author)