The Muon g - 2 collaboration has measured the anomalous magnetic g value of the positive muon with an uncertainty of 1.3 parts per million. The result alpha (+)mu (expt) = 11659202(14)(6) OE 10 exp -10, based on data collected in 1999 at Brookhaven National Laboratory, is in good agreement with the preceding data on alpha(+)mu and alpha(-)mu, and improves the combined uncertainty by a factor of about three. The analysis of data collected in 2000 and 2001 is well underway and, when combined with data from a requested final run in the fall of 2002 and winter of 2003, is expected to further improve the experimental uncertainty by a factor of about three to 0.4 ppm. The measurement tests standard theory and has the potential to discover new physics. (Author)