The textbook is designed for a semester-long course in *Foundations of geometry* and meant to be rigorous, conservative, elementary and minimalist.
It is based on lectures for course MATH 427 given at the Penn State University.

You can order a printed copy at amazon. Its exact copy can be downloaded at arXiv; printings of this (third) edition start with v16.

In addition to the traditional exercises in the book, one can use visual assignments.

Introduction

1. Preliminaries

Euclidean geometry

2. The Axioms

3. Half-planes

4. Congruent triangles

5. Perpendicular lines

6. Similar triangles

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.

Write me if you see a mistake.

Download the source files
and use it as you want, see the license below.