  Our calculation of the total cross section for inclusive production of
$t\bar{t}$ pairs in hadron collisions is presented. The principal ingredient of
the calculation is resummation of the universal leading-logarithm effects of
gluon radiation to all orders in the quantum chromodynamics coupling strength,
restricted to the region of phase space that is demonstrably perturbative. We
derive the perturbative regime of the resummed series, starting from the
principal-value resummation approach, and we isolate the perturbative domain in
both moment space and, upon inversion of the corresponding Mellin transform, in
momentum space. We show that our perturbative result does not depend on the
manner non-perturbative or infrared effects are handled in principal-value
resummation. We treat both the quark-antiquark and gluon-gluon production
channels consistently in the $\overline{{\rm MS}}$ factorization scheme. We
compare our method and results with other resummation methods that rely on the
choice of infrared cutoffs. We derive the renormalization/factorization scale
dependence of our resummed cross section, and we discuss factorization scheme
dependence and remaining theoretical uncertainties, including estimates of
possible non-perturbative contributions. We include the full content of the
exact next-to-leading order calculation in obtaining our final results. We
present predictions of the physical cross section as a function of top quark
mass in proton-antiproton reactions at center-of-mass energies of 1.8 and 2.0
TeV. We also provide the differential cross section as a function of the
parton-parton subenergy.
