  This article establishes the algebraic covering theory of quandles. For every
connected quandle we explicitly construct a universal covering, which in turn
leads us to define the algebraic fundamental group as the automorphism group of
the universal covering. We then establish the Galois correspondence between
connected coverings and subgroups of the fundamental group. Quandle coverings
are thus formally analogous to coverings of topological spaces, and resemble
Kervaire's algebraic covering theory of perfect groups. A detailed
investigation also reveals some crucial differences, which we illustrate by
numerous examples.
  As an application we obtain a simple formula for the second (co)homology
group of a quandle Q. It has long been known that H_1(Q) = H^1(Q) =
\Z[\pi_0(Q)], and we construct natural isomorphisms H_2(Q) = \pi_1(Q,q)_{ab}
and H^2(Q,A) = Ext(Q,A) = Hom(\pi_1(Q,q),A), reminiscent of the classical
Hurewicz isomorphisms in degree 1. This means that whenever the fundamental
group is known, (co)homology calculations in degree 2 become very easy.

Geometric Topology