ABSTRACT
The aim of the present chapter is to describe the universal knot invariant discovered independently by S.V. Matveev [Matv3] and D. Joyce [Joy]. In Matveev’s work and in other works by Russian authors, this invariant is usually called the distributive grouppoid; in Western literature it is usually called quandle.1 This invariant is a complete one;2 however, it is barely recognisable. In the present chapter, we shall construct some series of “weaker” invariants coming from the knot quandle; the series of invariants to be constructed are easier to calculate and to compare. We shall tell about so-called Conway algebras, describing them according to [PT]. Both these directions, the knot quandle and the Conway algebras, allow us to construct various knot invariants.
