© 2011

Foundations of Incidence Geometry

Projective and Polar Spaces

  • The book is a reference in which a lot of classical material is presented in most readable and accessible way

  • Valuable contribution to the literature about a wonderful piece of mathematics

  • Can be used by students, researchers and lecturers


Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Johannes Ueberberg
    Pages 1-56
  3. Johannes Ueberberg
    Pages 57-81
  4. Johannes Ueberberg
    Pages 83-122
  5. Johannes Ueberberg
    Pages 123-183
  6. Johannes Ueberberg
    Pages 185-244
  7. Back Matter
    Pages 245-248

About this book


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

Authors and affiliations

  1. 1., Mathematisches InstitutUniversität GießenGießenGermany

Bibliographic information

  • Book Title Foundations of Incidence Geometry
  • Book Subtitle Projective and Polar Spaces
  • Authors Johannes Ueberberg
  • Series Title Springer Monographs in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-642-20971-0
  • Softcover ISBN 978-3-642-26960-8
  • eBook ISBN 978-3-642-20972-7
  • Series ISSN 1439-7382
  • Edition Number 1
  • Number of Pages XII, 248
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
  • Buy this book on publisher's site


“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)