Hyperbolic Geometry from a Local Viewpoint (Hardcover)

Introduction; 1. Elementary transformations; 2 Hyperbolic metric in the unit disk; 3. Holomorphic functions; 4. Topology and uniformization; 5. Discontinuous groups; 6 Fuchsian groups; 7. General hyperbolic metric; 8. The Kobayashi metric; 9. The Caratheodory pseudo metric; 10. Contraction properties; 11. Applications; 12 Applications II; 13. Applications III; 14. Estimating hyperbolic densities; 15. Uniformly perfect domains; 16 Appendix: Elliptic functions; Bibliography.