Knot Theory

The Geometry Junkyard: Knot Theory - A page of links on geometric questions arising from knot embeddings.
http://www.ics.uci.edu/~eppstein/junkyard/knot.html

Knot Theory Invariants: The HOMFLY Polynomial - A brief article on the HOMFLY polynomial and how it is calculated.
http://library.thinkquest.org/12295/data/Invariants/Articles/HOMFLY.html

Thomas Fink (Tie Knots) - Thomas Fink and Yong Mao, used ideas from statistical mechanics to show there are 85 ways to tie a tie. They discovered a number of new aesthetically pleasing tie knots. This page has links to their original papers and to their book ``The 85 Ways to Tie a Tie''.
http://www.tcm.phy.cam.ac.uk/~tmf20/

A Circular History of Knot Theory - Starting with the flawed theory of Kelvin's knotted vortex to the work of Thurston, Jones and Witten, knot theory has circled back to its ancestral origins of theoretical physics.
http://www.math.buffalo.edu/~menasco/Knottheory.html

Knot Theory - An overview of knot theory from Mathworld
http://mathworld.wolfram.com/topics/KnotTheory.html

Knotscape - By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
http://www.math.utk.edu/~morwen/knotscape.html

Harmonic Knots - An introduction to harmonic knots. Gives (parametric) formulas for knots of up to 7 crossings.
http://www.carthage.edu/~trautwn/

A Knot Theory Primer - Comprehensive knot theory site focusing on the knot classification problem and knot tabulations. Has a tabulation of knots with up to 12 crossings.
http://www.inst.bnl.gov/~wei/contents.html

A Third Year Lecture Course on Knots - Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.
http://www.maths.warwick.ac.uk/~bjs/MA3F2-page.html

History of Knot Theory - Biographies of early knot theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson.
http://www.maths.ed.ac.uk/~aar/knots/index.htm

Knot Theory Group University of Liverpool - Links to preprints and to programs written in pascal for doing knot calculations.
http://www.liv.ac.uk/~su14/knotgroup.html

Morwen Thistlethwaite's Home Page - Has many beautiful images of symmetric knots, and information about a computer program called Knotscape (compiled binaries for Linux, Sunos and Alpha platforms). Includes pictures of knots with 13 crossings or less.
http://www.math.utk.edu/~morwen/

String Figure Mathematics (or Trivial Knot Theory) - A mathematical analysis of string figures. Theorems, examples, illustrations and conjectures on patterns created with an unknotted string.
http://website.lineone.net/~m.p/sf/menu.html

Using Topology to Probe the Hidden Action of Enzymes - Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy. [PDF]
http://www.ams.org/notices/199505/sumners.pdf

The Knot Theory Home Page - Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.
http://library.thinkquest.org/12295/

Cook's Borromean Ring Links - Links to pages and two outlines of proofs that show the Borromean rings can't be made from circular rings.
http://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.html

Geometry and the Imagination - Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.
http://math.dartmouth.edu/~doyle/docs/gi/gi/gi.html

New Knot Tables - Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos.
http://members.tripod.com/vismath7/knotab/

Knot Plot - A collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a program to visualize and manipulate mathematical knots in three and four dimensions.
http://www.pims.math.ca/knotplot/

Pictures of Knots - A table of graphics of all knots of up to nine crossings. Also includes pictures of some links.
http://www.math.unl.edu/~mbrittenham2/ldt/table9.gif

Megamath Knot Theory Page - An introductory overview of knot theory.
http://www.c3.lanl.gov/mega-math/gloss/knots/knots.html

Mathematics and Knots Exhibition - High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory.
http://www.bangor.ac.uk/cpm/exhib/

Knot Theory - Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations.
http://www.mapleapps.com/categories/mathematics/Knot%20theory/html/Knots.htm