  We present a study of top quark polarization in $t \overline{t}$ events
produced in $p \overline{p}$ collisions at $\sqrt{s}=1.96$ TeV. Data correspond
to 9.7 fb$^{-1}$ collected with the D0 detector at the Tevatron. We use final
states containing a lepton and at least three jets. The polarization is
measured using the distribution of leptons along the beam and helicity axes,
and the axis normal to the production plane. This is the first measurement of
top quark polarization at the Tevatron in $\ell$+jets final states, and first
measurement of transverse polarization in $t \overline{t}$ production. The
observed distributions are consistent with the standard model.
