  We define a quandle variety as an irreducible algebraic variety $Q$ endowed
with an algebraically defined quandle operation $\rhd$. It can also be seen as
an analogue of a generalized affine symmetric space or a regular $s$-manifold
in algebraic geometry.
  Assume that $Q$ is normal as an algebraic variety and that the action of the
inner automorphism group has a dense orbit. Then we show that there is an
algebraic group $G$ such that each orbit is isomorphic to the quandle $(G/H,
\rhd_\varphi)$ associated to the group $G$, an automorphism $\varphi$ of $G$
and a subgroup $H$ of $G^\varphi$.
