Combinatorial Geometry, by Janos Pach and Pankaj K. Agarwal. 1995, John Wiley and Sons.
I like this book a lot!
"On Thurston's formulation and proof of Andreev's theory," in Lecture Notes in Mathematics, no. 1435, Springer-Verlag, 1990
I have both of these out from the library, but I will return them tomorrow (and keep copies of the articles in my office).
A proof of the planar graph theorem may be found here.