  We summarize calculations of the cross section for top quark production at
hadron colliders within the context of perturbative quantum chromodynamics,
including resummation of the effects of initial-state soft gluon radiation to
all orders in the strong coupling strength. In our approach we resum the
universal leading-logarithm contributions, and we restrict the calculation to
the region of phase space that is demonstrably perturbative. We compare our
approach with other methods. We present predictions of the physical cross
section as a function of the top quark mass in proton-antiproton reactions at
center-of-mass energies of 1.8 and 2.0 TeV, and we discuss estimated
uncertainties.
