  We compute the Schroedinger functional (SF) for the case of pure SU(3) gauge
theory at two-loop order in lattice perturbation theory. This allows us to
extract the three-loop beta-function in the SF-scheme. These results are
required to compute the running coupling, the Lambda-parameter and quark masses
by finite size techniques with negligible systematic errors. In addition, we
can now implement two-loop O(a) improvement in simulations and extend and study
series in alternative ("tadpole-improved") bare couplings.
