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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.
 
A Dynamic Approach to Calculating the HOMFLY Polynomial for Directed Knots and Links - A research paper describing an algorithm for calculating the HOMFLY polynomial of directed knots and links. The algorithm has a better time bound for large links than algorithns that ignore duplicates. Source code is on the site.
 
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.
 
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.
 
An Introduction to Knot Theory - Introductory level tutorial requiring only a high school mathematics background, some linear algebra is needed in places.
 
BraidLink - Braidlink is software for knot and braid theory computations. It performs both analytic and numerical manipulations of knots and braids.
 
Cook's Borromean Ring Links - Links to pages about Borromean rings and two outlines of proofs that show the Borromean rings can't be made from circular rings.
 
Does the Jones Polynomial Detect Unknottedness? - Research paper (in postscript format) showing that any knot with trivial Jones polynomial must have at least 18 crossings. The number of different Alexander, Homfly and Jones polynomials for knots of up to 15 crossings is given.
 
Geometry and the Imagination - Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.
 
Harmonic Knots - An introduction to harmonic knots. Gives (parametric) formulas for knots of up to 7 crossings.
 
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.
 
Is String Theory in Knots? - A chapter from the book Event-Symmetric Space-Time discussing knots, braids and quantisation.
 
Kauffmman, Louis H - A topologist working in knot theory discusses the connection between knot theory and statistical mechanics. Sections on cybernetics and knots, Fourier knots and the author's research papers.
 
Knot Polynomials - Research paper on a state-space representation of the HOMFLY polynomial. Links to the paper in pdf,dvi and ps formats.
 
Knot Theory Group University of Liverpool - Links to preprints and to programs written in pascal for doing knot calculations.
 
Knot Theory Invariants: The HOMFLY Polynomial - A brief article on the HOMFLY polynomial and how it is calculated.
 
Knot Theory and Quantum Gravity - Quantizing general relativity brings knot theory into quantum gravity. The Jones polynomial is shown to give rise to physical states of quantum gravity. Links to research papers by the author.
 
Knots in Braid Notation - Listing of every knot of up to 11 crossings in braid notation. Useful for computer calculations in knot theory.
 
Knots on the Web - A collection of knotting resources.
 
Knotscape - By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
 
 

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