Includes bibliographical references (pages 233-237) and index.
1. Translation groups -- 2. Euclidean and hyperbolic geometry -- 3. Sphere geometries of Mobius and Lie -- 4. Lorentz transformations.
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Presents the real inner product spaces of arbitrary (finite or infinite) dimension greater than or equal to 2. This book studies the sphere geometries of Mobius and Lie for these spaces, besides euclidean and hyperbolic geometry, as well as geometries where Lorentz transformations play the key role.