This text is designed as an introduction to finite geometry for the undergraduate student. It could be used for second or third year students with some aptitude for, but not necessarily a great deal of background in, mathematics. A second year general student would have a good foundation in synthetic geometry with the completion of the first four chapters. A third year honours student or a fourth year student could be expected to complete the book in a one year course.

As far as background is concerned, only a fundamental knowledge of functions and set theory to the first year university level is essential. Some linear algebra and field theory would be useful for some parts of chapters 5, 6 and 7, but at a minimal level.

Listed in the last section of each chapter are forty to fifty exercises. Some of these are designed to consolidate the student's acquaintance with the concepts presented in the chapter. Others give additional results and introduce new concepts. The exercises form an important part of the material and I would strongly advise that students be assigned several each week. The very difficult problems have been starred.

The material presented in the book is based on the notion of ‘connection number’ in a near-linear space. Given a system of points and lines, for any point p not on a line ℓ, the connection number, c(p,ℓ), is the number of points on ℓ which are connected to p by a line. In chapter 1 (near-linear spaces) there are no restrictions on c(p,ℓ).