Foreword; Guide; 1. Maps; 2. Real and complex numbers; 3. Linear spaces; 4. Affine spaces; 5. Quotient structures; 6. Finite-dimensional spaces; 7. Determinants; 8. Direct sum; 9. Orthogonal spaces; 10. Quaternions; 11. Correlations; 12. Quadric Grassmannians; 13. Clifford Algebras; 14. The Cayley algebra; 15. Normed linear spaces; 16. Topological spaces; 17. Topological groups and manifolds; 18. Affine approximation; 19. The inverse function theorem; 20. Smooth manifolds; 21. Triality; Bibliography; List of symbols; Index.
Provides a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford's geometric algebras taking pride of place.
Taken from the hardback review: '... a remarkable book, which is likely to remain very useful, both for teaching and research, during many years to come.' J.Dieudonne in Zentralblatt Fur Mathematik