This work provides an introduction to the theory and main results of parabolic geometries, for graduate students and research mathematicians interested in parabolic geometry, conformal geometry, almost quaternionic structures, and CR-structures. The basic theme of the book is canonical Cartan connections associated with certain types of geometric structures. Two introductory chapters give background on Cartan geometries, and semisimple Lie algebras and their representations. The main part of the book discusses the equivalence between Cartan connections and underlying structures, including a complete proof of Kostant's version of the Bott-Borel-Weil theorem, which is used as an important tool. For many examples, the complete description of the geometry and its basic invariants is worked out in detail. The last chapter studies Weyl structures. Several applications are discussed throughout the text. A proposed future volume will cover invariant differential operators and applications. Cap is affiliated with Universität Wien, Austria. Slovák is affiliated with Masaryk University, Brno, Czech Republic. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)