The purpose of this paper is to bring together a few topics in know theory. To discuss the classical branch of knot theory, where the not groups are defined, we make the necessary topological and algebraic developments. The van Kampen theorem is stated and used to find knot groups in the traditional way, and also in a fashion that standard texts do not discuss. later developments in knot theory, for example the Jones polynomial, are also discussed, giving the reader the opportunity to see newer theory along with the old. We conclude by noting the incomplete state of affairs in knot theory: the lack of a perfect invariant.
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