Sub-boards: 1 The Tractrix and the Pseudosphere, 2 The constant curvature of the Pseudosphere*, 3 A Conformal Map of the Pseudosphere, 4 Beltrami's Hyperbolic Plane, 5 Hyperbolic Lines and Reflections, 6 The Bolyai-Lobachevsky Formula*, 7 The Three Types of Direct Motion, 8 Decomposition into Two Reflections, 9 The Angular Excess of a Hyperbolic Triangle, 10 The Poincaré Disc, 11 Motions of the Poincaré Disc, 12 The Hemisphere model and Hyperbolic Space