  The problem of ordering operators has afflicted quantum mechanics since its
foundation. Several orderings have been devised, but a systematic procedure to
move from one ordering to another is still missing. The importance of
establishing relations among different orderings is demonstrated by Wick's
theorem (which relates time ordering to normal ordering), which played a
crucial role in the development of quantum field theory. We prove the General
Ordering Theorem (GOT), which establishes a relation among any pair of
orderings, that act on operators satisfying generic (i.e. operatorial)
commutation relations. We expose the working principles of the GOT by simple
examples, and we demonstrate its potential by recovering two famous algebraic
theorems as special instances: the Magnus expansion and the
Baker-Campbell-Hausdorff formula. Remarkably, the GOT establishes a formal
relation between these two theorems, and it provides compact expressions for
them, unlike the notoriously complicated ones currently known.
