  We present a geometrically oriented classification theory for non-Abelian
extensions of groupoids generalizing the classification theory for Abelian
extensions of groupoids by Westman as well as the familiar classification
theory for non-Abelian extensions of groups by Schreier and Eilenberg-MacLane.
As an application of our techniques we demonstrate that each extension of
groupoids $\mathcal{N} \to \mathcal{E} \to \mathcal{G}$ gives rise to a
groupoid crossed product of $\mathcal{G}$ by the groupoid ring of $\mathcal{N}$
which recovers the groupoid ring of $\mathcal{E}$ up to isomorphism.
Furthermore, we make the somewhat surprising observation that our
classification methods naturally transfer to the class of groupoid crossed
products, thus providing a classification theory for this class of rings. Our
study is motivated by the search for natural examples of groupoid crossed
products.
