I. Preliminaries -- 1. Quaternions -- 2. The hyperbolic functions -- 3. Trace relations -- 4. The fractional linear group and the cross ratio -- Notes to Chapter I -- II. The Möbius Group -- 1. Similarity transformations -- 2. The extended space. Orientation. Angular measure -- 3. Inversion -- 4. Circle- and sphere-preserving transformations -- 5. The Möbius group of the upper half-space -- Notes to Chapter II -- III. The Basic Notions of Hyperbolic Geometry -- 1. Lines and planes. Convexity -- 2. Orthogonality -- 3. The invariant Riemannian metric -- 4. The hyperbolic metric -- 5. Transformation to the unit ball -- Notes to Chapter III -- IV. The Isometry Group of Hyperbolic Space -- 1. Characterization of the isometry group -- 2. Classification of the motions -- 3. Reversals -- 4. The isometry group of a plane -- 5. The spherical and cylindric surfaces -- Notes to Chapter IV -- V. Lines -- 1. Line matrices -- 2. Oriented lines -- 3. Double crosses -- 4. Transversals -- 5. Pencils and bundles of lines -- Notes to Chapter V -- VI. Right-Angled Hexagons -- 1. Right-angled hexagons and pentagons -- 2. Trigonometric relations for right-angled hexagons -- 3. Trigonometric relations for polygons in a plane -- 4. Determination of a hexagon by three of its sides -- 5. The amplitudes of a right-angled hexagon -- 6. Transversals of a right-angled hexagon -- 7. The bisectors and radii of a right-angled hexagon -- 8. The medians of a right-angled hexagon -- 9. The altitudes of a right-angled hexagon -- Notes to Chapter VI -- VII. Points and Planes -- 1. Point and plane matrices -- 2. Incidence and orthogonality -- 3. Distances and angles -- 4. Pencils of points and planes -- 5. Bundles of points and planes -- 6. Tetrahedra -- Notes to Chapter VII -- VIII. Spherical Surfaces -- 1. Equations of spherical surfaces.

2. An invariant of a pair of spherical surfaces -- 3. The power of a point with respect to a spherical surface -- 4. The radical plane of a pair of spherical surfaces -- 5. Linear families of spherical surfaces -- Notes to Chapter VIII -- IX. Area and Volume -- 1. Various coordinate systems -- 2. Area -- 3. Volume of some bodies of revolution -- 4. Volume of polyhedra -- Notes to Chapter IX -- References -- Index.