PART I
1. Early Geometry
2. Euclidean Geometry and the Parallel Postulate
3. Investigations by Islamic Mathematicians
PART II
4. Saccheri and his Western Predecessors
5. J.H. Lambert's Work
6. Legendre's Work
7. Gauss' Contribution
8. Trigonometry
9. The First New Geometries
10. The Discoveries of Lobachevskii and Bolyai
11. Curves and Surfaces
12. Riemann on the Foundations of Geometry
13. Beltrami's Ideas
14. New Models and Old Arguments
15. Resume
PART III
16. Non-Euclidean Mechanics
17. The Question of Absolute Space
18. Space, Time, and Space-Time
19. Paradoxes of Special Relativity
20. Gravitation and Non-Euclidean Geometry
21. Speculations
22. Some Last Thoughts