Good introductory texts:
The knot book by Colin Adams
Knots Knotes by Justin Roberts
Two Lectures On The Jones Polynomial And Khovanov Homology, by Edward Witten. An advanced gauge theory approach.
An introduction to knot Floer homology, by Ciprian Manolescu.
The Trieste look at knot theory, by Jozef Przytycki.
Introduction to knots and a survey of knot colorings.
3-coloring and other elementary invariants of knots, by Jozef Przytycki.
Short review of braids, by
Dale Rolfsen.
An Introduction
to braid theory, by Maurice Chiodo.
An elementary introduction
to the theory of braids, by Roger Fenn.
About the Temperley-Lieb algebra: by
V.S.Sunder,
Anne Moore,
Dana Emst.
Topological invariants of knots: three routes to the Alexander polynomial, by Edward Long.
Knot theory and the Alexander polynomial, by Reagin McNeill.
Data on knots and their invariants:
The Knot Atlas (wiki),
by Dror Bar-Natan and Scott Morrison. Among other info, it contains
Rolfsen's table
of knots up to 10 crossings.
Table of Knot Invariants, by Charles Livingston
and Jae Choon Cha.
The KnotPlot Site
SnapPy.
The CompuTop.org Software Archive, a site for people doing computational stuff with low-dimensional topology.
Other knot theory books:
Knot theory, a book by Vassily Manturov.
On knots, by Louis Kauffman;
Formal knot theory, by Louis Kauffman;
Knots and physics, by Louis Kauffman;
Knot theory, by Charles Livingston;
Introduction to knot theory, by R.Crowell and R.Fox;
A survey of knot theory, by A.Kawauchi;
Braids, links and mapping class groups, by Joan Birman.