This volume presents 16 contributions from the workshop of the same name (held at the Mathematics Institute, U. of Warwick, UK in September 2001). The first group of papers include Yair Minsky's lectures on the combinatorial part of his efforts to extend his results on Thurston's ending lamination conjecture for once-punctured tori to general surfaces, along with other articles on the geometry of hyperbolic 3-manifolds. Other papers revisit Troels Jo>rgensen's paper On pairs of once-punctured tori, also included here. A final trio of papers looks at related topics, including a counterexample to Thurston's K = 2 conjecture, and Schwarz's lemma and the Kobayashi and Carathéodory pseudometrics on complex Banach manifolds.