The algebraic theory of quandles

Quandle coloring provides an interesting knot invariant which is particularly useful for the algorithmic treatment of the knot equivalence problem. In the lecture, I will explain the algebraic tools that can be used to construct and enumerate various types of quandles suitable for knot coloring, including Joyce's classification of simple quandles, a group theoretic approach to connected quandles, and a universal algebraic approach to solvability and nilpotence for quandles.