  The mass of the bottom quark can be determined with high precision from
moments of the pair-production cross section sigma(e+ e- -> b bbar) near
threshold. We present the first complete NNNLO determination from
non-relativistic sum rules, obtaining a bottom-quark mass of mb^PS(2 GeV) =
(4.532 +0.013 -0.039) GeV in the potential-subtracted scheme. For the mass in
the MSbar scheme we find mb^MS(mb^MS) = (4.203 +0.016 -0.034) GeV using the
recently computed four-loop correction to the scheme conversion.
