David A. Brannan is Emeritus Professor in the Department of Mathematics and Computing at The Open University, Milton Keynes. Matthew F. Esplen is a Lecturer in the Department of Mathematics and Statistics at The Open University, Milton Keynes. Jeremy J. Gray is a Professor of the History of Mathematics at The Open University, Milton Keynes and Honorary Professor at the University of Warwick.

• Preface; Introduction: geometry and geometries; 1. Conics; 2. Affine geometry; 3. Projective geometry: lines; 4. Projective geometry: conics; 5. Inversive geometry; 6. Hyperbolic geometry: the disc model; 7. Elliptic geometry: the spherical model; 8. The Kleinian view of geometry; Special symbols; Further reading; Appendix 1. A primer of group theory; Appendix 2. A primer of vectors and vector spaces; Appendix 3. Solutions to the problems; Index.

'This is a textbook that demonstrates the excitement and beauty of geometry … richly illustrated and clearly written.' L'Enseignement Mathématique