  In this paper, we consider a theory of gravity with a metric-dependent
torsion namely the $F(R,T)$ gravity, where $R$ is the curvature scalar and $T$
is the torsion scalar. We study a geometric root of such theory. In particular
we give the derivation of the model from the geometrical point of view. Then we
present the more general form of $F(R,T)$ gravity with two arbitrary functions
and give some of its particular cases. In particular, the usual $F(R)$ and
$F(T)$ gravity theories are the particular cases of the $F(R,T)$ gravity. In
the cosmological context, we find that our new gravitational theory can
describes the accelerated expansion of the universe.
