Hertrich-Jeromin introduces students to the geometry of surfaces and submanifolds in the conformal sphere using various models. He starts with "the Reimannian point of view" and proceeds to the projective model (with a brief description of sphere congruences and their envelopes) and two applications, the first for conformally flat hypersurfaces and the second for isothermic and Willmore surfaces. He continues by describing a quaternionic model and application and a Clifford algebra model and application, thoughtfully providing the classical model of Möbius geometry in table form for reference. Annotation ©2005 Book News, Inc., Portland, OR (booknews.com)