  The recently proposed MUonE experiment at CERN aims at providing a novel
determination of the leading order hadronic contribution to the muon anomalous
magnetic moment through the study of elastic muon-electron scattering at
relatively small momentum transfer. The anticipated accuracy of the order of
10ppm demands for high-precision predictions, including all the relevant
radiative corrections. To aid the effort, the theoretical formulation for the
fixed order NNLO QED corrections are described and the virtual NNLO leptonic
corrections are calculated with complete mass effects.
