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, an

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). 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) Several key takeaways: 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. 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. 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.