Essentials of the muon g-2

The muon anomalous magnetic moment is one of the most precisely measured quantities in particle physics. Recent high precision measurements (0.54 ppm) at Brookhaven reveal a ''discrepancy'' by 3 standard deviations from the electroweak Standard Model which could be a hint for an unknown contribution from physics beyond the Standard Model. This triggered numerous speculations about the possible origin of the ''missing piece''. The remarkable 14-fold improvement of the previous CERN experiment, actually animated a multitude of new theoretical efforts which lead to a substantial improvement of the prediction of aμ. The dominating uncertainty of the prediction, caused by strong interaction effects, could be reduced substantially, due to new hadronic cross section measurements in electron-positron annihilation at low energies. After an introduction and a brief description of the principle of the experiment, I present a major update and review the status of the theoretical prediction and discuss the role of the hadronic vacuum polarization effects and the hadronic light-by-light scattering contribution. Prospects for the future are briefly discussed. As, in electroweak precision physics, the muon g-2 shows the largest established deviation between theory and experiment at present, it will remain one of the hot topics for further investigations. (orig.)