Anderson, J. W.
(2005)
*Hyperbolic geometry, second revised edition*
(Springer Undergraduate Mathematics Series),
London, UK.
Springer Verlag London Ltd, 276pp.

## Abstract

This is an undergraduate textbook covering the basics of planar hyperbolic geometry. Topics covered include the upper half-space model of the hyperbolic plane, Mobius transformations, the general Mobius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincare disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications. This updated second edition also features: an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; the hyperboloid model of the hyperbolic plane; a brief discussion of generalizations to higher dimensions; and many new exercises.

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