  This paper develops explicit class field theory for orders: of rank 1 in any
global function field -- Hayes theory -- and of rank 2 in real quadratic
function fields -- Real Multiplication. The essential ingredient in the
development of the Hayes Theory is an orders version of Shimura's Main Theorem
on Complex Multiplication. The section on Real Multiplication for orders uses
values of the quantum modular invariant to generate the Hilbert class field of
a rank 2 order contained in the integral closure of $\mathbb{F}_{q}[T]$.
