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.

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 7. G-morphisms 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 Index

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