This research monograph covers extensively the theory of the muon anomalous magnetic moment and provides estimates of the
theoretical uncertainties. The muon anomalous magnetic moment is one of the most precisely measured quantities in elementary
particle physics and provides one of the most stringent tests of relativistic quantum field theory as a fundamental theoretical
framework. It allows for an extremely precise check of the standard model of elementary particles and of its limitations.
This book reviews the present state of knowledge of the anomalous magnetic moment a=(g-2)/2 of the muon. Recent experiments
at the Brookhaven National Laboratory now reach the unbelievable precision of 0.5 parts per million, improving the accuracy
of previous g-2 experiments at CERN by a factor of 14. In addition, quantum electrodynamics and electroweak and hadronic effects
are reviewed. Since non-perturbative hadronic effects play a key role for the precision test, their evaluation is described
in detail. Perspectives for future improvements of the theoretical and experimental precision are considered. The new edition
features improved theoretical predictions to match upcoming experiments, like the one at Fermilab. Additionally the new more
precise basic parameters are presented.