Geometry from a Differentiable Viewpoint (Paperback)

Prelude and themes; Part I. Synthetic Methods and Results: 1. Spherical geometry; 2. Euclid; 3. The theory of parallels; 4. Non-Euclidean geometry I; 5. Non-Euclidean geometry II; Part II. Development: Differential Geometry: 6. Curves; 7. Curves in space; 8. Surfaces; 9. Curvature for surfaces; 10. Metric equivalence of surfaces; 11. Geodesics; 12. The Gauss?Bonnet theorem; 13. Constant curvature surfaces; Part III. Recapitulation; 14. Abstract surfaces; 15. Modelling non-Euclidean geometry; 16. Coda: generalizations.