This is a graduate textbook about how to color graphs.  Each chapter studies a single method, and presents numerous examples applying that method, generally in order of increasing difficulty. The book is designed to be suitable for a topics course in graph coloring, as well as self-study. The chapters are listed below.

1.  Greedy Coloring
2.  Gadgets: Constructions for Lower Bounds
3.  Recoloring
4.  Vertex Identification: Coloring Planar Graphs
5.  The Kernel Method
6.  Deletion and Contraction: Nowhere-Zero Flows
7.  Rosenfeld Counting
8.  The Combinatorial Nullstellensatz
9.  The Activation Strategy
10.  The Vertex Shuffle
11.  Precoloring Extension
12.  The Potential Method
13.  The Rest of the Story

This book is (and always will be) freely available for download.  It is released under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  License details are available at https://creativecommons.org/licenses/by-nc-nd/4.0.

If you would like a paperback version, you can purchase one on Amazon. In the United States, it costs $24. It is also available in other markets: US  CA  UK  FR  IT  ES  DE  AU  NL  PL  SE  JP