Knot Theory

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

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

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

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 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/

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

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

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

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

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

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

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

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

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/

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

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

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

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/

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