TITLE: Proofs of circle packing theorem
QUESTION [8 upvotes]: Circle packing theorem is a famous result stating that for every connected simple planar graph $G$ there is a circle packing in the plane whose intersection graph is $G$ https://en.wikipedia.org/wiki/Circle_packing_theorem.
I know that this result has many proofs and I want to read one of them, but don't understand how to start (for quite a while). The article in wiki gives a reference to Thurston notes, but the proof comes only in the last section and I am not sure if this is the simplest approach. I like these notes very much, but was never able to read them till the end. So I wonder if there are some simple proofs of this result nowadays. Can you advise something?

REPLY [3 votes]: Books are written on the subject, so, finding a proof (which are many by now) shouldn't be a problem. I also enjoyed greatly Rohde's tribute to Schramm that explains in very nice way some ideas that Schramm introduced into the area; following references from there one should be able to find more detailed accounts.