I Finite Geometries. - 1 Introduction via the Fano Plane. - 2 Designs. - 3 Configurations. - 4 Generalized Quadrangles. - 5 The Smallest Three-Dimensional Projective Space. - 6 The Projective Plane of Order 3. - 7 The Projective Plane of Order 4. - 8 The Projective Plane of Order 5. - 9 Stargazing in Affine Planes up to Order 8. - 10 Biplanes. - 11 Semibiplanes. - 12 The Smallest Benz Planes. - 13 Generalized Polygons. - 14 Colour Pictures and Building the Models. - 15 Some Fun Games and Puzzles. - II Geometries on Surfaces. - 16 Introduction via Flat Affine Planes. - 17 Flat Circle PlanesAn Overview. - 18 Flat Projective Planes. - 19 Spherical Circle Planes. - 20 Cylindrical Circle Planes of Rank 3. - 21 Toroidal Circle Planes. - A Models on Regular Solids. - B Mirror Technique Stereograms. - B. 1 The Generalized Quadrangle of Order (42). - B. 3 The Smallest Projective Space. - References. Language: English