Classical knot theory is the study of smooth embeddings of circles in the 3-sphere up to the ambient isotopy. One of the fundamental problems in this field is the classification of knots, for which one needs invariants. The fundamental group of a knot complement space is a well-known invariant, but there are examples where it fails to distinguish knots. Around the 1980s, Matveev and Joyce introduced an almost complete knot invariant using quandles, known as knot quandles.

In the talk, I will introduce the notion of residual finiteness of quandles and prove that all link quandles are residually finite. Using the preceding result, we will see that the word problem is solvable for link quandles. I will talk about the orderability properties of link quandles. Since all link groups are left-orderable, it is reasonable to speculate that link quandles are left (right)-orderable. In contrast, we will see that the orderability of link quandles behave quite differently than that of the corresponding link groups.