Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author's experience in implementing geometric software and includes hundreds of high-quality illustrations.

Full Professor for Geometry and Visualization at Technical University Munich. Research in combinatorial, computational and dynamic geometry, automated geometric theorem proving and visualization. Author of the dynamic geometry program Cinderella and of the interactive visualization portal Mathe-Vital. Cinderella was awarded the Multimedia Innovation Award, the European Academic Software Award and the Deutsche Bildungssoftwarepreis. Mathe-Vital won the renowned MedidaPrix in 2008.