  We calculate the shear viscosity over entropy density ratio $\eta/s$ in
Yang--Mills theory from the Kubo formula using an exact diagrammatic
representation in terms of full propagators and vertices using gluon spectral
functions as external input. We provide an analytic fit formula for the
temperature dependence of $\eta/s$ over the whole temperature range from a
glueball resonance gas at low temperatures, to a high-temperature regime
consistent with perturbative results. Subsequently we provide a first estimate
for $\eta/s$ in QCD.
