Top Quark Production to ${\cal{O}}(\alpha_s^2)$

The cross-section for the production of $t\bar{t}$ pairs in $e^+e^-$-annihilation via a virtual photon is determined up to order $\alpha_s^2$. For the cm-energies of interest the effect of the top mass may not be considered as a small parameter and the full mass dependence must be included.