I am a knot theorist (PhD student) and always tickled when the subject pops up on HN. Curious what the author had in mind including this in his algebraic topology notes. Even the Jones polynomial which is both algebra and topology is not usually called "algebraic topology", but rather "quantum topology".
If anyone is interested in a conversational intro to the subject with lots of pictures, I suggest these semi-famous "Knots Knotes" (amazing title)