Using standard field theoretical techniques, we survey pure Yang-Mills theo
ry on the noncommutative torus, including Feynman rules and BRS symmetry. A
lthough in general free of any infrared singularity, the theory is ultravio
let divergent. Because of an invariant regularization scheme, this theory t
urns out to be renormalizable and the detailed computation of the one-loop
counterterms is given, leading to an asymptotically free theory. Besides, i
t turns out that nonplanar diagrams are overall convergent when theta is ir
rational.