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I found this book a bit too informal. A very easy introduction to Knot Theory, that is still mathematically rigorous is Cromwell's, one of the few books written explicitly for undergraduates. After you are about 1/3 of the way through, you can start using Lickorish. Combined they make the best introduction, by far.

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After 15 years of doing math, I've decided that, for myself, the best introduction isn't the one that's "rigorous" or "in-depth", it's the one the leaves you wanting to learn more. For me, that was Colin's book. I wish more topics in math had entry-level books that explicitly helped contextualize why certain questions were being asked, rather than defining undergraduate simply by what material is covered/how things are proved (of course, I ended up as an applied mathematician, so it could just be me).

I had a class with Adams while at Williams (multivariable Calculus, never got to take his Knot Theory class). He was a great teacher, and excellent about teaching students why they should care.

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