  We perform threshold resummation of soft gluon corrections to the total cross
section and the invariant mass distribution for the process $pp \to t\bar{t}H$.
The resummation is carried out at next-to-next-to-leading-logarithmic (NNLL)
accuracy using the direct QCD Mellin space technique in the three-particle
invariant mass kinematics. After presenting analytical expressions we discuss
the impact of resummation on the numerical predictions for the associated Higgs
boson production with top quarks at the LHC. We find that NLO+NNLL resummation
leads to predictions for which the central values are remarkably stable with
respect to scale variation and for which theoretical uncertainties are reduced
in comparison to NLO predictions.
