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1 Acknowledgement

I wish to thank the following individuals for help with various aspects of this project:

• Jana Archibald, for writing the program Alexander[K, r].

• Sergei Chmutov, for spotting a typo.

• David De Wit, for a bug report.

• Ralph Furmaniak, for help with our link to Knotilus (Section 4.2).

• Stavros Garoufalidis, for jointly writing the program ColouredJones (Section 7.6).

• Thomas Gittings, for the minimum braid representatives for the knots with up to 10 crossings (Section 4.4).

• Jeremy Green, for his java implementation of Kh (Section 7.11).

• Thang Le, for supplying some of the formulas used in the program ColouredJones (Section 7.6).

• Rick Litherland, for spotting a sneaky bug in the program KnotSignature.

• Charles Livingston, for allowing me to bundle data from his Table of Knot Invariants.

• Scott Morrison, for a bug report and for writing the programs to compute the HOMFLY-PT and Kauffman polynomials (Sections 7.8 and 7.9).

• Bertrand Patureau-Mirand, for informing me of some mismatches in the link tables (now corrected).

• Jozef Przytycki, for correcting a typo.

• Stuart Rankin, for help with our link to Knotilus (Section 4.2).

• Emily Redelmeier, for writing the program DrawPD (Section 5.1).

• Siddarth Sankaran, for writing the conversion program between Gauss codes and PD codes and for writing MorseLink and DrawMorseLink.

• Alexander Shumakovitch, for his help with signature computations (Section 7.4).

• Alexander Stoimenow, for the knot presentations for the knots in the Rolfsen table and some further remarks.

• Z-X. Tao, for noticing problems with the knots $10_{83}$ and $10_{86}$.

• Morwen Thistlethwaite, for the pictures of links and of 11 crossing knots.

• Dylan Thurston, for writing a routine to translate from Hoste-Thistlethwaite's DT codes to my ``PD Presentations'' (Section 4.1).