Visualizing the cross product between two vectors

The authors have a website - geometricalgebra.net - where you can download a program which will display all the diagrams from the book and allow you to manipulate them. You can also render arbitrary low-dimensional geometric algebra constructions which helps tremendously with improving your intuition about how things work. I'd say it's at a middle ground of mathematical sophistication - it's a good mix of proofs and practical usage. It's almost entirely dedicated to applying geometric algebra to computer graphics, so you won't get as much out of it if you're interested in applications to physics, or just pure mathematics.

If nothing else, I finally know what a quaternion really is after going through this book.