Free groups and presentations. Primary source: notes by Inna Bumagin. These notes were in turn based on notes by Alexei Myasnikov. Presentations of symmetric groups. Primary source: Johnson, Presentations of Groups (locked). Knot groups: Wirtinger presentations. Primary source: my own notes, which were based on Hatcher's text, p.55 or thereabouts. Quotients of knot groups. Primary source: Johnson, Homomorphs of knot groups (Proc. AMS 1980) (locked). Secondary sources: papers by GonzalezAcuna (locked), Neuwirth (locked). Groups generated by reflections. Primary source: Coxeter and Moser, Generators and Relations for Discrete Groups (locked). Changing presentations without changing the group (Tietze transformations, AndrewsCurtis moves). Primary sources: the Tietze transformations page at wikipedia.org; Rolfsen, The Poincare conjecture and its cousins. New groups from old: free products, amalgamations, graphs of groups, BassSerre theory. Primary source: Scott and Wall, Topological methods in group theory (locked). The PingPong Lemma, faithful representations of free groups. Primary sources: notes by Marc Culler on free groups (public), Macbeath, Packings, free products, and residually finite groups (locked). Valuations, the tree for SL_2(K), K a field with discrete valuation. Primary source: Shalen, Representations of 3manifold groups, preprint version (public), final version (locked). The tree for SL_2(Z). Primary source: Dicks and Dunwoody, Groups acting on graphs (locked). Linear representations of finitely presented groups. Primary source: Shalen, Representations of 3manifold groups. 3manifold groups acting on trees and incompressible surfaces. Primary sources: Stallings, Group theory and 3manifolds (locked); Shalen, Representations of 3manifold groups. Hyperbolic 3manifolds. Primary source: Thurston's Princeton notes (public), my own scanned, marked up copy (locked). Incompressible surfaces and boundary slopes. Primary source: haven't found a good reference yet. Secondary source: Hatcher, Boundary slopes of incompressible surfaces (locked), updated version (public). The Apolynomial. Primary sources: the two papers listed below. For an interpretation from the point of view of physics, look at a paper by Gukov (locked).
The papers/topics motivating all of this: Culler and Shalen, Varieties of Group Representations and Splittings of 3manifolds (locked). Cooper, Culler, Gillet, Long, and Shalen, Plane curves associated to character varieties of 3manifolds (locked). Cooper and Long, Representation Theory and the Apolynomial of a knot (locked). Shalen, Representations of 3manifold groups, chapter 19 of "Handbook of Geometric Topology (locked).
