  By a quantum metric space we mean a C^*-algebra (or more generally an
order-unit space) equipped with a generalization of the Lipschitz seminorm on
functions which is defined by an ordinary metric. We develop for compact
quantum metric spaces a version of Gromov-Hausdorff distance. We show that the
basic theorems of the classical theory have natural quantum analogues. Our main
example involves the quantum tori, $A_{\th}$. We show, for consistently defined
``metrics'', that if a sequence $\{\th_n\}$ of parameters converges to a
parameter $\th$, then the sequence $\{A_{\th_n}\}$ of quantum tori converges in
quantum Gromov-Hausdorff distance to $A_{\th}$.
