Introduction to Circle Packing: The Theory of Discrete Analytic Functions Book

I	An overview of circle packing	1
1	A circle packing menagerie	3
2	Circle packings in the wild	15
II	Rigidity : maximal packings	33
3	Preliminaries : topology, combinatorics, and geometry	35
4	Statement of the fundamental result	51
5	Bookkeeping and monodromy	54
6	Proof for combinatorial closed discs	62
7	Proof for combinatorial spheres	72
8	Proof for combinatorial open discs	73
9	Proof for combinatorial surfaces	116
III	Flexibility : analytic functions	131
10	The intuitive landscape	133
11	Discrete analytic functions	139
12	Construction tools	153
13	Discrete analytic functions on the disc	160
14	Discrete entire functions	181
15	Discrete rational functions	195
16	Discrete analytic functions on Riemann surfaces	201
17	Discrete conformal structure	217
18	Random walks on circle packings	232
IV	Resolution : approximation	247
19	Thurston's conjecture	249
20	Extending the Rodin-Sullivan theorem	257
21	Approximation of analytic functions	268
22	Approximation of conformal structures	275
23	Applications	286
App. A	Primer on classical complex analysis	309
App. B	The ring lemma	318
App. C	Doyle spirals	322
App. D	The Brooks parameter	327
App. E	Inversive distance packings	331
App. F	Graph embedding	335
App. G	Square grid packings	339
App. H	Schwarz and buckyballs	343
App. I	CirclePack	346