Although chances are slim the riff-raff down at their favorite pool hall will be impressed, serious students of differential geometry will find this one of the more accessible ways of describing the geodesic flow on manifold with boundary, and its relation to billiards in classical mechanics and geometrical optics. Topics include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and non-existence of caustics, optical properties of conics and quadrics, completely integrable billiards, periodic billiard trajectories, polygonal billiards, chaos and dual billiards. Although aimed at undergraduate audiences past the entire calculus sequence and linear algebra, this may require the mathematical common sense that is typical amongst the aforesaid riff-raff. Annotation ©2005 Book News, Inc., Portland, OR (booknews.com)