  We describe the calculation of the next-to-next-to-leading order (NNLO) QCD
corrections to three-jet production and related event shape observables in
electron-positron annihilation. Infrared singularities due to double real
radiation at tree level and single real radiation at one loop are subtracted
from the full QCD matrix elements using antenna functions, which are then
integrated analytically and added to the two loop contribution. Using this
antenna subtraction method, we obtain numerically finite contributions from
five-parton and four-parton processes, and observe an explicit analytic
cancellation of infrared poles in the four-parton and three-parton
contributions. All contributions are implemented in a flexible parton-level
event generator programme, allowing the numerical computation of any
infrared-safe observable related to three-jet final states to NNLO accuracy.
