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What would the best resources be for someone who wants to study self-avoiding walks from a mathematical standpoint?

I'm talking about seminal/important papers, good textbooks perhaps, things of that nature.

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There are recent lecture notes by Bauerschmidt, Duminil-Copin, Goodman, and Slade (arXiv:1206.2092). Most of the important papers should be in the references to that lecture notes, and it depends on your focus which of those to recommend. For the 2D case, you may look at

G.F. Lawler, O. Schramm, and W. Werner, On the scaling limit of planar self-avoiding walk.

H. Duminil-Copin and S. Smirnov, The connective constant of the hexagonal lattice equals 􏰀$\sqrt{2+\sqrt2}$.

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