"In topology, knot theory is the study of mathematical knots."
This is how Wikipedia defines knot theory. I have no idea what this is supposed to mean, but it does seem interesting. The rest of the article is full of examples of knots, their notation and such, which I understand a little bit better, but I still fail to understand why and how they are studied. So, what exactly is knot theory about?
What characteristics of knots are studied, and how does it connect to the rest of mathematics? Full disclosure: I have experience with analysis, know at least the basics of abstract algebra, and I think I could understand elementary topology. So feel free to give me only a moderately technical description.
