Racks and quandles are fundamental algebraic structures. Quandles have been rediscovered and studied extensively over the past sixty years [Br88,Deh00,GK03,Joy82,Kauff91,Mat82,Taka42]. It appears that a special case of quandles (involutory quandles), called Kei, first appeared in literature in [Taka42]. The name quandle is due to [Joy82]. It is beyond our scope here to review such a rich history of quandles in details.
In [CJKLS03], quandle cohomology theory was constructed
as a modification of rack cohomology theory [FRS95,FRS*], and
quandle cocycle invariants were also defined in a state-sum form.
It is our goal here to briefly review this invariant.