This volume presents the Oxford Mathematical Institute notes for the enormously successful advanced undergraduate and first-year graduate student course on groups and geometry. The book's content closely follows the Oxford syllabus but covers a great deal more material than did the course itself. The book is divided into two parts: the first covers the fundamentals of groups, and the second covers geometry and its symbiotic relationship with groups. Both parts contain a number of useful examples and exercises. This book will be welcomed by student and teacher alike as a lucidly written text on an important topic.
'develops a comprehensive group-theoretic approach to affine, projective and inversive geometry ... It ends with a fascinating chapter on the group theory behind the Rubik cube.'
Ian Stewart, New Scientist
'Both parts contain a number of exercises that will be invaluable to any reader wishing to gain a fuller understanding of this area of mathematics.'
Extrait de L'Enseignement Mathematique, T. 40 1994
The book can be recommended warmly for any interested reader. "Monatshefte fur Mathematik No.3 1996.
`delightful book ... The group theory is directed towards group actions, but all the basic material is there.'
Mathematika, 41 (1994)
1: A survey of some group theory
2: A menagerie of groups
3: Actions of groups
4: A garden of G-spaces
5: Transitivity and orbits
6: The classification of transitive G-spaces
8: Group actions in group theory
9: Actions count
10: Geometry: an introduction
11: The axiomatisation of geometry
12: Affine geometry
13: Projective geometry
14: Euclidean geometry
15: Finite groups of isometries
16: Complex numbers and quaternions
17: Inversive geometry
18: Topological considerations
19: The groups theory of Rubik's magic cube