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.
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.
