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I present calculations of approximate corrections from NNLL soft-gluonresummation for total and differential cross sections in top-antitop pairproduction and single-top production in hadronic collisions. I show thatsoft-gluon corrections from partonic threshold are the dominant contribution totop-quark production and closely approximate exact results. I present aN$^3$LOresults for the total $t{\bar t}$ cross section, the top-quark $p_T$ andrapidity distributions, and the top-quark forward-backward asymmetry. I alsoprovide updates for single-top production in the $t$, $s$, and $tW$ channels.Finally, I discuss top-quark production via anomalous gluon couplings.

N$^3$LO calculations for top-quark differential cross sections near partonic threshold