Theory of Lepton g-2:  Improvement of QED Terms.






  All 469 $\alpha^4$ terms which depend on the electron-muon mass ratio

have been evaluated in two or more independent formulations. Evaluation of many

$\alpha^5$ terms are in progress. Uncertainties in both $\alpha^4$ and $\alpha^5$

terms have been reduced substantially, eliminating QED as a possible source of

theoretical uncertainty in the muon g-2.