The Knot Book (Google eBook) 
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Review: The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
User Review  Philip Rideout  GoodreadsThis book is a rarity because it sits exactly at the right level of math for me: it's advanced enough to feel like a real mathematics book with theories and equations and whatnot, but it's still much ... Read full review
Review: The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
User Review  Jon  GoodreadsCovers a large number of topics (eg analysis, algebra, topology) without assuming much background. Provides lots of interesting things to think about, and will often gloss over the technical details ... Read full review
Common terms and phrases
Alexander polynomial alternating knot alternating link amphicheiral axis boundary component bracket polynomial braid index called circle closed braid color composite knot compute conjecture corresponding crossing change crossing number curve deformed Dehn surgery denote dichromatic polynomial disk edges embedding enzyme equation Euler characteristic Exercise fact fewer crossings figureeight knot fourspace glue gluing HOMFLY polynomial hyperbolic knots integers intersection invariant isotopy Jones polynomial knot or link knot projection knot theory knots and links least number link projection linking number look loop manifold Math mathematics meridian mirror image Mobius band molecule nontrivial knot number of crossings obtain pair partition function picture planar graph prime knots proved rational tangle Reidemeister moves result satellite knot Seifert surface Seifert's algorithm sequence Show signed planar graph solid torus space sphere strands string tetrahedra threemanifold threespace threesphere tion topology torus knot trefoil knot tricolorable trivial knot trivial link twist unknot unknotting number vertex vertices