Wolfram Neutsch 
Coordinates [PDF ebook] 

I-XIV — Volume 1: Theory — 0. Introduction — A. Foundations. — 1. Historical development of the coordinate concept — 2. Notation and conventions — B. Geometry. — 3. Manifolds — 4. Riemannian spaces — 5. Applications to physics — 6. Complex analysis — 7. Projective Geometry — C. Rotations. — 8. Orthogonal groups — 9. Linear transformations of complex spaces — 10. Quaternions — 11. Octaves — 12. Hopf mappings — 13. Spinors — 14. Lorentz transformations — 15. Coxeter groups — 16. Invariant rings of finite Weyl groups — 17. Basic invariants — Volume 2: Applications — E. Lattices. — 18. Elliptic functions and modular forms — 19. Euclidean lattices — 20. Linear codes — 21. The Leech lattice — F. Spheres. — 22. Harmonic functions — 23. Spherical surface functions — 24. Lattice integration — 25. Spherical designs — G. Coordinate systems. — 26. Linear and reducible coordinates — 27. Three-dimensional Stackel coordinates — 28. Confocal Coordinates — 29. Gauß-Krüger Coordinates — 30. Coordinates for special applications — H. Tables. — Calculation and organization of the tables — Coordinates in R2 — Coordinates in R3 — Coordinates in R4 — Appendix. References — Appendix. Index