Chapter 1. Book overview
Part 1. Surfaces and topology
Chapter 2. Definition of a surface
Chapter 3. The gluing construction
Chapter 4. The fundamental group
Chapter 5. Examples of fundamental groups
Chapter 6. Covering spaces and the deck group
Chapter 7. Existence of universal covers
Part 2. Surfaces and geometry
Chapter 8. Euclidean geometry
Chapter 9. Spherical geometry
Chapter 10. Hyperbolic geometry
Chapter 11. Riemannian metrics on surfaces
Chapter 12. Hyperbolic surfaces
Part 3. Surfaces and complex analysis
Chapter 13. A primer on complex analysis
Chapter 14. Disk and plane rigidity
Chapter 15. The Schwarz-Christoffel transformation
Chapter 16. Riemann surfaces and uniformization
Part 4. Flat cone surfaces
Chapter 17. Flat cone surfaces
Chapter 18. Translation surfaces and the Veech group
Part 5. The totality of surfaces
Chapter 19. Continued fractions
Chapter 20. Teichmüller space and moduli space
Chapter 21. Topology of Teichmüller space
Part 6. Dessert
Chapter 22. The Banach–Tarski theorem
Chapter 23. Dehn’s dissection theorem
Chapter 24. The Cauchy rigidity theorem