  The results of phenomenological studies of top-quark pair production in
proton-proton collisions are presented. Differential cross sections are
calculated in perturbative QCD at approximate next-to-next-to-leading order
${\cal O}(\alpha_s^4)$ by using methods of threshold resummation beyond the
leading logarithmic accuracy. Predictions for the single-particle inclusive
kinematics are presented for transverse momentum and rapidity distributions of
final-state top quarks. Uncertainties related to the description of proton
structure, top-quark mass and strong coupling constant are investigated in
detail. The results are compared to the recent measurements by the ATLAS and
CMS collaborations at the LHC at the center of mass energy of 7 TeV. The
calculation presented here is implemented in the computer code \textsc{Difftop}
and can be applied to the general case of heavy-quark pair production at
hadron-hadron colliders. For the first time, a fit of parton distribution
functions at NNLO is performed by using the differential cross sections of
top-quark pair production together with other data sets. The impact of the
top-pair production on the precision of the gluon distribution at high scales
is illustrated.
