  The complete 2-loop quantum electrodynamic corrections to the muon lifetime
are calculated in the Fermi theory. The exact result for the effects of virtual
and real photons, virtual electrons, muons as well as e+e- pair creation is
  Delta Gamma_QED
  = Gamma_0(alpha/pi)^2[(156815/5184)-(1036/27)zeta(2)-(895/36)zeta(3)
  +(67/8)zeta(4)+53zeta(2)ln(2)]
  = Gamma_0(alpha/pi)^2(6.743)
  where Gamma_0 is the tree-level width. The theoretical error in the value of
the Fermi coupling constant, G_F, is now rendered negligible compared to the
experimental uncertainty coming from the measurement of the muon lifetime. The
overall error in G_F is then roughly halved giving
  G_F = (1.16637 +/- 0.00001) x 10^(-5) GeV^(-2).
