An Introduction to the Discharging Method via Graph Coloring

We provide a "how-to" guide to the use and application of the Discharging Method. Our aim is not to exhaustively survey results proved by this technique, but rather to demystify the technique and facilitate its wider use, using applications in graph coloring as examples. Along the way, we present some new proofs and new problems.
Comment: We shortened the paper (now 50 pages, originally 78). This version omits total, entire, and improper coloring, as well as linear choosability. It spends less time on circular, acyclic, and star coloring, along with linear arboricity. (For those topics, see the first version.) We significantly reorganized the first few sections. We feel that the result is more accessible and inviting