The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist.

You can order a printed copy at amazon. Its exact copy can be downloaded at arXiv. (The older printings start from [v11]; the numbering of some statements has been changed).

Visual assignments can be used in addition to the traditional exercises in the book.

Introduction

1. Preliminaries

Euclidean geometry

2. The Axioms

3. Half-planes

4. Congruent triangles

5. Perpendicular lines

6. Similar triangless

7. Parallel lines

8. Triangle geometry

Inversive geometry

9. Inscribed angles

10. Inversion

Non-Euclidean geometry

11. Neutral plane

12. Hyperbolic plane

13. Geometry of h-plane

Additional topics

14. Affine geometry

15. Projective geometry

16. Spherical geometry

17. Projective model

18. Complex coordinates

19. Geometric constructions

20. Area

Write me a short message if you are teaching a course using this book. Also, write me if you see a mistake.

You can download the source files
and use it as you want, see the license below.