  We implement a noncommutative analogue of the well-known commutative cyclic
covering trick and implement it to explicitly construct a vast collection of
numerically Calabi-Yau orders, noncommutative analogues of surfaces of Kodaira
dimension 0. We construct maximal orders, noncommutative analogues of normal
schemes, on rational surfaces and ruled surfaces. We also use Ogg-Shafarevich
theory to construct Azumaya algebras and, more generally, maximal orders on
elliptically fibred surfaces.
