  We present the first direct determination of the running top-quark mass based
on the total cross section of top-quark pair-production as measured at the
Tevatron. Our theory prediction for the cross section includes various
next-to-next-to-leading order QCD contributions, in particular all
logarithmically enhanced terms near threshold, the Coulomb corrections at two
loops and all explicitly scale dependent terms at NNLO accuracy. The result
allows for an exact and independent variation of the renormalization and
factorization scales. For Tevatron and LHC we study its dependence on all
scales, on the parton luminosity and on the top-quark mass using both the
conventional pole mass definition as well as the running mass in the MSbar
scheme. We extract for the top-quark an MSbar mass of m(mu=m) = 160.0 +3.3 -3.2
GeV, which corresponds to a pole mass of m_t = 168.9 +3.5 -3.4 GeV.
