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The following is a list of comments and errata. Not all typographical errors are included here. (p. = Page, e. = Exercise, l. = Line, t. = Theorem, c. = Corollary, f. = Figure, d. = Definition.)

• p.10, e.7: The deformation is quite difficult to find; Perko's paper, listed in the references, has a series of figures illustrating it.
• p. 13, l 20, Change "Figure 2.3" to "Figure 2.2".
• p.26, e.5.5: Here "inversion" means a deformation of the knot to its reverse.
• p.32, e.1.2: Deform the illustrated knot into a standard picture of the unknot, using only Reidemeister moves.
• p.35, e.2.2: n is the number of half twists; for example, in Figure 3.6a, n is the number of crossings.
• p.36, e.2.4b: Theorem 2, not Theorem 1. e.2.4d: Theorem 2, not Theorem 1. Also, in Figure 3.7 the diagram on the left illustrates a right-handed crossing.
• p.43, f.3.13: The numbers of the crossings were omitted. They are easily discovered using the matrix lower on the page.
• p.51, f.3.16: The numbers of the crossings were again omitted; they should be numbered 1, 2, and 3, beginning at the top.
• p.52, l.5 & l.17: n must be odd to get a knot. To generalize the formula to apply in the case of links, add (-1)^n and (-1)^(n-1) factors in front of the t's.
• p.53, l.1: Exercise 4.2, not 4.3.
• p.65, l.19: The details of the proof are called for in Exercise 2.3, not 4.3.
• p.79, l.8 & l.21: The proof calls on Corollary 2, at these points, not Corollary 3.
• p.88, e.1.7b: (1,5,3,4) is the product of three transpositions, not four.
• p.91, f.5.2: The (2 3) label should be elevated to mark the short arc.
• p.94, e.2.2: Only one of the labelings is correct, not two.
• p.97, l.30: Knot 6_1 cannot be labeled with transposition, but can be labeled with 4-cycles. Knot 9_46 can be labeled in both ways, not just with transpositions. (The point remains the same; these knots are distinguished using S_4 labelings only if the conjugacy classes of labels are considered.)
• p.99, e.3.4: See comment, p.97.
• p.104, e.4.1: The second relation is clearly wrong. Check the relations on p.101.
• p.106, l.8: Figure 5.10 is not the trefoil knot.
• p.110, l.23 & l.24: Exercises 2.5 and 2.6, not 2.4 and 2.5.
• p.113, l.3: The (2,1) entry of the matrix is 0, not -5. e.1.3: Tthe 5-twisted double, not 3.
• p.117, l.3: The *'s in the matrix represent possibly distinct unknown entries.
• p.118, l.2: The matrix M can have determinant 1 or -1.
• p119, l.22: The suggested exercise does not appear.
• p.121, l.24: The signature is 0, not 2. l.27: With respect to the basis we have used earlier, the matrix would have +1 on the off-diagonal, not -1.
• p.123, e.3.9: Reference should be Exercise 1.5, not 2.5.
• p.124, l.4: The construction appears in Chapter 5, not 4.
• p.125, l.16: The "equation" should be set equal to 1.
• p.140, e.3.4: One can assume p is always positive. In this case, the knots are equivalent if and only if q - q' = 0 mod p, or qq' = 1 mod p.
• p.146, t.2: Should read brg(K) greater than or equal to n-1, not n.
• p.153, l.12: For a 3-stranded pretzel knot with all twist numbers odd, the knot is reversible only if two of the twist numbers are equal. If one of the twist numbers is even the knot is always reversible.
• p.154, d.: The last clause, "or reflection through the (y,x) plane," should be deleted.
• p.157, f.8.7: The top right figure, though correct, would be better "flipped" to match the top left figure.
• p.159, l.4: Exercise 2.5, not 2.6.
• p.165, l.8 & l.10: For the first case, lambda is 2, and in the next 3.
• p.175, l.2: The (1,-3,5)-pretzel knot is the knot 8_1, not 7_2.
• p.183, l.18: The cross-sections of the (2,4)-torus link, not the trefoil, are illustrated.
• p.196, t.2: The determinant may be -1 or +1.
• p.197, c.4: The statement and proof are correct for the signature. However, the omega-signatures may be nonzero for any values of omega that are roots of the Alexander polynomial. (In given argument, for such omega the relevant matrix is not invertible.)
• p.216, l.11: Exercise 1.3, not 1.6. e.2.3: This holds for all links. e.2.5: Refers to Exercise 1.7, not 1.5.
• p. 218 l. -6, Change t^{-5} + t^{-3} + t^{-7} to -t^{-5} - t^{-3} + t^{-7}.
• p.236, l.4: The reference is to the article "A polynomial invariant for knots and links via von Neumann algebras.
• p.239: Several references are off by one page, and there have been good suggestions for added references. Contact me directly for an update.

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