Lectures on Riemann Surfaces (Paperback, Softcover Repri)

1 Covering Spaces.- 1. The Definition of Riemann Surfaces.- 2. Elementary Properties of Holomorphic Mappings.- 3. Homotopy of Curves. The Fundamental Group.- 4. Branched and Unbranched Coverings.- 5. The Universal Covering and Covering Transformations.- 6. Sheaves.- 7. Analytic Continuation.- 8. Algebraic Functions.- 9. Differential Forms.- 10. The Integration of Differential Forms.- 11. Linear Differential Equations.- 2 Compact Riemann Surfaces.- 12. Cohomology Groups.- 13. Dolbeault's Lemma.- 14. A Finiteness Theorem.- 15. The Exact Cohomology Sequence.- 16. The Riemann-Roch Theorem.- 17. The Serre Duality Theorem.- 18. Functions and Differential Forms with Prescribed Principal Parts.- 19. Harmonic Differential Forms.- 20. Abel's Theorem.- 21. The Jacobi Inversion Problem.- 3 Non-compact Riemann Surfaces.- 22. The Dirichlet Boundary Value Problem.- 23. Countable Topology.- 24. Weyl's Lemma.- 25. The Runge Approximation Theorem.- 26. The Theorems of Mittag-Leffler and Weierstrass.- 27. The Riemann Mapping Theorem.- 28. Functions with Prescribed Summands of Automorphy.- 29. Line and Vector Bundles.- 30. The Triviality of Vector Bundles.- 31. The Riemann-Hilbert Problem.- A. Partitions of Unity.- B. Topological Vector Spaces.- References.- Symbol Index.- Author and Subject Index.