Generalized Polygons (Monographs in Mathematics, Vol 93)

"Generalized Polygons" is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. "Generalized Polygons" will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the literature very often considered separately - to polygons. Many alternative viewpoints given in the book heighten the sense of beauty of the subject and help to provide further insight into the matter.

"... If you believe that incidence geometry is out of date, this book will prove you wrong. If you are interested in geometry and want to get introduced to fascinating recent concepts, this book will be a good starting point and a trustworthy companion for most of your way. If you are already doing research in incidence geometry, this book will bring you up to date on generalized polygons and provide a very convincing notation. In addition, its bibliography and its almost complete collection of results on generalized polygons will make it an indispensable tool. If you are eager to do some research, the author offers ten open problems."

–Zentralblatt Math