This textbook is a very accessible introduction to projective geometry based on lectures given at the University of Adelaide. The book assumes a familiarity with linear algebra, elementary group theory, partial derivatives, finite fields and elementary coordinate geometry, hence it is suitable for students in their third or fourth year at university. The beginning of the book is devoted to Desargues’ theorem, which plays a key role in projective geometry. In the following chapters, the author introduces the reader to axiomatic geometry and defines the field plane PG(2,F) and its higher dimensional generalization PG(r,F). The author also considers projective spaces of dimension 2 (known as non-Desarguesian planes). The last chapters deal with conics and quadrics in PG(3, F). The textbook uses modern concepts of projective geometry closely related to algebra and algebraic geometry with the aim of helping the reader to understand and master proof techniques. An attractive feature of the book is a number of solved examples and more than 150 exercises.

Reviewer:

jol