  We determine the four Fermi effective theory of neutrino interactions within
the Standard Model including one-loop electroweak radiative corrections, in
combination with the measured muon lifetime and precision electroweak data.
Including two-loop matching and three-loop running corrections, we determine
lepton coefficients accounting for all large logarithms through relative order
$\cal{O}(\alpha \alpha_s)$ and quark coefficients accounting for all large
logarithms through ${\cal{O}}(\alpha)$. We present four-fermion coefficients
valid in $n_f=3$ and $n_f=4$ flavor quark theories, as well as in the extreme
low-energy limit. We relate the coefficients in this limit to neutrino charge
radii governing matter effects via forward neutrino scattering on charged
particles.
