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 Geometry -- 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 -- References -- Hints -- Index -- Used resources

This book is meant to be rigorous, conservative, elementary and minimalist. At the same time it includes about the maximum what students can absorb in one semester. Approximately one-third of the material used to be covered in high school, but not any more.The present book is based on the courses given by the author at the Pennsylvania State University as an introduction to the foundations of geometry. The lectures were oriented to sophomore and senior university students. These students already had a calculus course. In particular,they are familiar with the real numbers and continuity. It makes it possible to cover the material faster and in a more rigorous way than it could be done in high school.

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In English.

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