Top positive review
This book contained the stuff I wanted to know
Reviewed in the United States on May 9, 2003
I was interested in projecting a network onto hyperbolic space using the upper half plane projection. This book contained the equations relating to that, particularly the moebius transformation z' = (az+b) / (cz + d), and also stuff on stereographic mapping which I found useful.
I have not taken the trouble to understand much of the more in-depth parts of the book, but it is so clear and step-by-step that even though I am not a math student, I'm fairly confident that I could. The whole thing was fairly mind-opening.
Interestingly, after reading this and developing my own intuitions (eg: that flat translation, rotation and scaling are special cases of parabolic, elliptical and hyperbolic transformations with a fixed point at infinity), a re-reading discovered these conclusions in the book. So you can take the exposition and run with it. What I'd really like is to be able to get the n'th root of a transformation (to animate them). I suspect that that's in there too.
The book does not cover real-world applications (aerodynamics, electrodynamics), but that's cool. It's purely about the math.