In ongoing and upcoming hadron collider experiments, top quark physics
will play an important r\^ole in testing the Standard Model and its
possible extensions.
In this work we present analytic results for the differential
cross sections of top quark pair production
in hadronic collisions at next-to-leading order
in the QCD coupling, keeping the full dependence on the spins of the top
quarks.
These results are combined with the corresponding next-to-leading
order results for the
decay of polarized top quarks into dilepton, lepton plus jets, and
all jets final states.
As an application we predict double differential angular
distributions which are due to the QCD-induced top quark spin
correlations in the intermediate state. In addition to the analytic
results, we give numerical
results in terms of fit functions that can easily be
used in an experimental analysis.