The two-loop electroweak radiative corrections to the muon's anomalous
magnetic moment, a(mu) = (g(mu) - 2)/2, are presented. We obtain an o
verall 22.6% reduction in the electroweak contribution alpha mu(BW) fr
om 195 x 10(-11) to 151(4) x 10(-11). Implications for the full standa
rd model prediction and an upcoming high precision measurement of alph
a(mu) are briefly discussed. Some aspects of the calculations are disc
ussed in detail.