  We argue that Yang-Mills theory on noncommutative torus, expressed in the
Fourrier modes, is described by a gauge theory in a usual commutative space,
the gauge group being a generalization of the area-preserving diffeomorphisms
to the noncommutative case. In this way, performing the loop calculation in
this gauge theory in the continuum limit we show that this theory is {\it one
loop renormalizable}, and discuss the UV and IR limits. The moduli space of the
vacua of the noncommutative super Yang-Mills theories in (2+1) dimensions is
discussed.
