  In this paper, we investigate residual finiteness and subquandle separability
of quandles. The existence of these finiteness properties implies the
solvability of the word problem and the generalised word problem for quandles.
We prove that the fundamental $n$-quandle of any link in the 3-sphere is
residually finite for each $n \ge 2$. This supplements the recent result on
residual finiteness of link quandles and the classification of links whose
fundamental $n$-quandles are finite for some $n$. We also establish several
general results on these finiteness properties and give many families of
quandles admitting them.
