The structure of the book.

Notation.

1 Introduction.

2 The World of Space and Time.

2.1 Timetable.

2.2 Surveying Space–Time.

2.3 Physical Prerequisites of Geometry.

3 Reflection and Collision.

3.1 Geometry and Reflection.

3.2 The Reflection of Mechanical Motion.

4 The Relativity Principle of Mechanics and Wave Propagation.

5 Relativity Theory and its Paradoxes.

5.1 Pseudo-Euclidean Geometry.

5.2 Einstein’s Mechanics.

5.3 Energy.

5.4 Kinematic Peculiarities.

5.5 Aberration and Fresnel’s Paradox.

5.6 The Net.

5.7 Faster than Light.

6 The Circle Disguised as Hyperbola.

7 Curvature.

7.1 Spheres and Hyperbolic Shells.

7.2 The Universe.

8 The Projective Origin of the Geometries of the Plane.

9 The Nine Geometries of the Plane.

10 General Remarks.

10.1 The Theory of Relativity.

10.2 Geometry and Physics.

Appendices.

A Reflections.

B Transformations.

B.1 Coordinates.

B.2 Inertial Reference Systems.

B.3 Riemannian Spaces, Einstein Worlds.

C Projective Geometry.

C.1 Algebra.

C.2 Projective Maps.

C.3 Conic Sections.

D The Transition from the Projective to the Metrical Plane.

D.1 Polarity.

D.2 Reflection.

D.3 Velocity Space.

D.4 Circles and Peripheries.

D.5 Two Examples.

E The Metrical Plane.

E.1 Classification.

E.2 The Metric.

Exercises.

Glossary.

References.