New: Updated drafts of chapters (last updated 10 Apil 2017).
Posted here are drafts of some of the current chapters. I'm very interested in feedback from students and other mathematicians.
 Introduction [pdf]
 Decomposition of the figure8 knot [pdf]
 Calculating in hyperbolic space [pdf]
 Geometric structures on manifolds [pdf]
 Hyperbolic structures and triangulations [pdf]
 Discrete groups and the thickthin decomposition [pdf]
 Completion and Dehn filling [pdf]
 Twist knots [pdf]
 Essential surfaces
 Volume and angle structures
 Twobridge knots [pdf]
 Alternating knots
 Ford domains and canonical polyhedra
 Volume
 Representations and the Apolynomial
 Tunnel number one knots
 Bibliography and index [pdf]
