A non-mathematical, but much more practical resource, is the Ashley Book of Knots (fondly known as "ABOK"). Clifford Ashley was a sailor who collected knots, and an accomplished painter and writer. If you find yourself in New Bedford, MA, you can see some of his work in the whaling museum (which I highly recommend).<p>I took a knot theory class as an undergrad, and I don't remember which book we used. It ended up being a pretty superficial introduction to the subject, which is both disappointing, and probably also how I got my first "A" in a math class since 11th grade (which, I would argue, was wholly undeserved)<p>Several key takeaways:<p>1. The figure 8 knot is the only 4 crossing knot. If you climb, and use it as your tie-in, you can check that you've tied it correctly by checking that you have 5 pairs of strands in the knot.<p>2. The figure 8 knot is amphichiral. There appear to be two variants (like the left and right-handed trefoil knot), but they are transformable into each other via the "pretzel" configuration, which seems to be the canonical representation in math.<p>3. If you coil rope with only overhand or underhand loops and pull it out, you put a lot of twist into it. If you alternate overhand and underhand loops, it pulls out untwisted. This is most easily seen with ribbon, which has two distinct sides.