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# Geometries

### About this Title

**A. B. Sossinsky**, *Independent University of Moscow, Moscow, Russia*

Publication: The Student Mathematical Library

Publication Year
2012: Volume 64

ISBNs: 978-0-8218-7571-1 (print); 978-0-8218-8788-2 (online)

DOI: http://dx.doi.org/10.1090/stml/064

MathSciNet review: MR2951761

MSC: Primary 51-01; Secondary 01A20, 01A55, 51-02, 51M10, 51N99

### Table of Contents

**Front/Back Matter**

**Chapters**

- Chapter 0. About Euclidean geometry
- Chapter 1. Toy geometries and main definitions
- Chapter 2. Abstract groups and group presentations
- Chapter 3. Finite subgroups of $SO(3)$ and the platonic bodies
- Chapter 4. Discrete subgroups of the isometry group of the plane and tilings
- Chapter 5. Reflection groups and Coxeter geometries
- Chapter 6. Spherical geometry
- Chapter 7. The Poincaré disk model of hyperbolic geometry
- Chapter 8. The Poincaré half-plane model
- Chapter 9. The Cayley–Klein model
- Chapter 10. Hyperbolic trigonometry and absolute constants
- Chapter 11. History of non-Euclidean geometry
- Chapter 12. Projective geometry
- Chapter 13. “Projective geometry is all geometry”
- Chapter 14. Finite geometries
- Chapter 15. The hierarchy of geometries
- Chapter 16. Morphisms of geometries
- Appendix A. Excerpts from Euclid’s “Elements”
- Appendix B. Hilbert’s axioms for plane geometry
- Answers & hints