This is an undergraduate textbook that reveals the intricacies of geometry. The approach used is that a geometry is a space together with a set of transformations of that space (as argued by Klein in his Erlangen programme). The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case the key results are explained carefully, and the relationships between the geometries are discussed. This richly illustrated and clearly written text includes full solutions to over 200 problems, and is suitable both for undergraduate courses on geometry and as a resource for self study.

- Cover
- Half Title
- Title Page
- Copyright
- Dedication
- Contents
- Preface
- 0. Introduction: Geometry and Geometries
- 1. Conics
- 2. Affine Geometry
- 3. Projective Geometry: Lines
- 4. Projective Geometry: Conics
- 5. Inversive Geometry
- 6. Non-Euclidean Geometry
- 7. Spherical Geometry
- 8. The Kleinian View of Geometry
- Appendix 1: A Primer of Group Theory
- Appendix 2: A Primer of Vectors and Vector Spaces
- Appendix 3: Solutions to the Problems
- Index