Classical Geometries in Modern Contexts

This book is based on real inner product spaces of arbitrary (finite or infinite) dimension greater than or equal to 2. For these spaces the sphere geometries of Mobius and Lie are studied, besides Euclidean and hyperbolic geometry, as well as geometries where Lorentz transformations play the key role. A real benefit is the dimension-free approach to important geometrical theories. The only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry. Designed as a two-term graduate course the book helps students to understand great ideas of classical geometries in a modern and general context.