This is an undergraduate textbook that reveals the intricacies of geometry. The approach used is that a geometry is a space together with a set of transformations of that space (as argued by Klein in his Erlangen programme). The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case the key results are explained carefully, and the relationships between the geometries are discussed. This richly illustrated and clearly written text includes full solutions to over 200 problems, and is suitable both for undergraduate courses on geometry and as a resource for self study.

‘This is a textbook that demonstrates the excitement and beauty of geometry … richly illstrated and clearly written.’

Source: Extrait de L’Enseignement Mathématique

‘ … this is a remarkable and nicely written introduction to classical geometry.’

Source: Zentralblatt MATH

‘ … could form the basis of courses in geometry for mathematics undergraduates. It will also appeal to the general mathematical reader.’

John Stone Source: The Times Higher Education Supplement