1. Neutral Geometry. Introduction. Axioms of Incidence and Betweenness. Convex Sets. Measuring Segments and Angles. Congruence of Triangles. The Circle. Principles of Continuity. The Basic Geometric Constructions.
2. Euclidean Plane Geometry. Euclid's Fifth Postulate. Euclidean Triangles. Similar Triangles. Euclidean Circles. Trigonometric Functions. Euclidean Constructions.
3. Geometric Transformations. Rigid Motions. Similarities. Inversions. Coordinate Systems. Appendix.
4. Euclidean 3-Space. Axiom System for 3-Dimensional Geometry. Perpendicular Lines and Planes. Rigid Motions in 3-Space. Vectors in 3-Space.
5. Euclidean n-Space. The n-Space. Basis and Change of Coordinates. Linear Transformations. Orthogonal Transformations. Orthogonal transformations of
R2 and
R3. Orientation.
6. Perimeter, Area and Volume. Perimeter and Circumference. Area of Polygonal Regions. Area of Circles. Volumes.
7. Spherical Geometry. Arc Length. Metric Spaces. Spherical Distance and Its Isometries. Geodesics and Triangles on Spheres. Conformal Maps. Appendix.
8. Hyperbolic Geometry. Introduction. Neutral Geometry Revisited. The Hyperbolic Parallel Postulate. Classification of Parallels. The Angle of Parallelism. Defect of Hyperbolic Triangles.
9. Models for Plane Geometries. Introduction. The Poincarè Models. A Note on Elliptic Geometry.
10. The Hyperbolic Metric. Introduction. The Complex Plane. Analytic Functions. Geometric Transformations. Classification of Isometries. The Hyperbolic Metric. Hyperbolic Triangles. Hyperbolic Circles.
List of Axioms. Index. 