The determination of the Fermi coupling constant, G_F, is examined in the
light of recently calculated 2-loop QED corrections and planned experiments to
measure the muon lifetime to a level below 1ppm. The methods used in the
calculation of the QED corrections are described in detail. Sources of the
dominant theoretical and experimental uncertainties are identified. Finally the
incorporation of G_F into analyses using the full electroweak Standard Model is
discussed.Comment: 48 pages LaTeX. 11 figures. Uses amsmath.sty, axodraw.sty, cite.st
