Topological, Differential and Conformal Geometry of Surfaces (2021)

-1. Basic Differential Geometry.- 2. The Geometry of Manifolds.- 3. Hyperbolic Geometry.- 4. Some Examples and Sources of Geometry.- 5. Differential Topology of Surfaces.- 6. Riemann Surfaces.- 7. Surfaces of Genus g = 0.- 8. Surfaces with Riemannian Metric.- 9. Outline: Uniformization by Spectral Determinant.- 10. Uniformization by Energy.- 11. Families of Spaces.- 12. Functions on Riemann Surfaces.- 13. Line Bundles and Cohomology.- 14. Moduli Spaces and Teichmüller Spaces.- 15. Dimensions of Spaces of Holomorphic Sections.- 16. The Teichmüller Curve and its Universal Property.- 17. Riemann Surfaces and Algebraic Curves.- 18. The Jacobian of a Riemann Surface.- 19. Special Metrics on J-Surfaces.- 20. The Fundamental Group and Coverings.- A. Reminder: Topology.- References.- Index.