Springer Monographs in Mathematics / Foundations of Incidence Geometry

I Projective and Affine Geometries .- 1. Introduction.- 2. Geometries and Pregeometries.- 3. Projective and Affine Planes.- 4. Projective Spaces.- 5. Affine Spaces.- 6. A Characterization of Affine Spaces.- 7. Residues and Diagrams.- 8. Finite geometries.- II Isomorphisms and Collineations .- 1. Introduction.- 2. Morphisms.- 3. Projections.- 4. Collineations of projective and affine spaces.- 5. Central Collineations.- 6. The Theorem of Desargues.- III Projective Geometry over a Vector Space .- 1. Introduction.- 2. The Projective Space P(V).- 3. Homogeneous Coordinates of Projective Spaces.- 4. Automorphisms of P(V).- 5. The Affine Space AG(W).- 6. Automorphisms of A(W).- 7. The First Fundamental Theorem.- 8. The Second Fundamental Theorem.- IV Polar Spaces and Polarities .- 1. Introduction.- 2. The Theorem of Buekenhout-Shult.- 3. The diagram of a polar space.- 4. Polarities.- 5. Sesquilinear Forms.- 6. Pseudo-quadrics.- 7. The Kleinian Polar Space.- 8. The Theorem of Buekenhout and Parmentier.- V Quadrics and Quadratic Sets .- 1. Introduction.- 2. Quadratic Sets.- 3. Quadrics.- 4. Quadratic Sets in PG(3, K).- 5. Perspective Quadratic Sets.- 6. Classification of the Quadratic Sets.- 7. The Kleinian Quadric.- 8. The Theorem of Segre.- 9. Further Reading.- References.- Index.

"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." (György 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)