This textbook is intended as an introduction to the combinatorial theory of finite geometry for undergraduate students of mathematics. Although only a basic knowledge of set theory and analysis is assumed, the student is soon led Op results at the frontiers of research. Professor Batten begins with a discussion of near-linear spaces before proceeding to treat linear, projective and affine spaces. This half of the book in itself would be suitable for use as a text for a course in synthethic geometry. The remainder of the book is devoted to the relatively new areas of polar spaces, generalized quadrangles and partial geometries. These subjects are currently the focus of much research in combinatorial geometry.
This is my favorite finite geometry text. The treatment is a mixture of basic and complex and is hence suitable for a wise variety of readers, probably best for undergraduate/beginning graduate courses, but works well for self-study. I am excited about the generalized quadrangles sections.
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