Foundations of Incidence Geometry

Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces.

Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout.

The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.

• projective and affine geometry
• 51E24, 51A05, 51A50
• buildings
• coxeter geometries
• diagram geometry
• polar spaces

“This book provides an introduction into projective and affine spaces as well as polar spaces in the modern language of diagram geometry. … The book is well written and contains many enlightning pictures. It is mainly directed to students.” (Hans Cuypers, Nieuw Archief voor Wiskunde, Issue 4, December, 2015)

“The book under review is a comprehensive monograph devoted to the foundations of incidence geometry … . a clear and good introduction for graduate students who want to learn about modern geometry and is also useful for lecturers who offer courses on this topic. The book may also be of interest for researchers because it contains several results which were previously only available in the original research articles. … At the end of the book the author gives some hints about further reading too.” (Gyӧrgy Kiss, Mathematical Reviews, November, 2013)

“The book contains almost all classical results from projective geometry. It is written in a readable style. Especially the first two chapters can be recommended to those who are interested in a synthetic treatment of projective geometry.” (Boris Odehnal, Zentralblatt MATH, Vol. 1237, 2012)

• , Mathematisches Institut, Universität Gießen, Gießen, Germany

  Johannes Ueberberg

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