  This article is the second part of a series of three articles, in which we
develop a higher covering theory of racks and quandles. This project is rooted
in M. Eisermann's work on quandle coverings, and the categorical perspective
brought by V. Even, who characterizes coverings as those surjections which are
central, relatively to trivial quandles. We extend this work by applying the
techniques from higher categorical Galois theory, in the sense of G. Janelidze,
and in particular we identify meaningful higher-dimensional centrality
conditions defining our higher coverings of racks and quandles. In this first
article (Part I), we revisit and clarify the foundations of the covering theory
of interest, we extend it to the more general context of racks and
mathematically describe how to navigate between racks and quandles. We explain
the algebraic ingredients at play, and reinforce the homotopical and
topological interpretations of these ingredients. In particular we justify and
insist on the crucial role of the left adjoint of the conjugation functor Conj
between groups and racks (or quandles). We rename this functor Pth, and explain
in which sense it sends a rack to its group of homotopy classes of paths. We
characterize coverings and relative centrality using Pth, but also develop a
more visual ``geometrical'' understanding of these conditions. We use
alternative generalizable and visual proofs for the characterization of central
extensions of racks and quandles. We complete the recovery of M. Eisermann's ad
hoc constructions (weakly universal cover, and fundamental groupoid) from a
Galois-theoretic perspective. We sketch how to deduce M. Eisermann's detailed
classification results from the fundamental theorem of categorical Galois
theory. We lay down all the ideas and results which will articulate the
higher-dimensional theory developed in Part II and III.
