We perform a new calculation of the hadronic contributions, a(Hadronic) to the anomalous magnetic moment of the muon, aµ. For the low energy contributions of order α 2 we carry over an analysis of the pion form factor Fπ(t) using recent data both on e + e − → π + π − and τ + →ντ π + π 0 . In this analysis we take into account that the phase of the form factor is equal to that of ππ scattering. This allows us to profit fully from analyticity properties so we can use also experimental information on Fπ(t) at spacelike t. At higher energy we use QCD to supplement experimental data, including the recent measurements of e + e − → hadrons both around 1 GeV and near thecc threshold. This yields a precise determination of the O(α 2 ) and O(α 2 ) + O(α 3 ) hadronic part of the photon vacuum polarization pieces, 10 11 × a (2) (h.v.p.) = 6 909 ± 64; 10 11 × a (2+3) (h.v.p.) = 7 002 ± 66 As byproducts we also get the masses and widths of the ρ 0 , ρ + , and very accurate values for the charge radius and second coefficient of the pion.Adding the remaining order α 3 hadronic contributions we find 10 11 × a theory (Hadronic) = 6 993 ± 69 (e + e − + τ + spacel.)The error above includes statistical, systematic and estimated theoretical errors. The figures given are obtained including τ decay data; if we restrict ourselves to e + e − data, slightly lower values and somewhat higher errors are found. This is to be compared with the figure obtained by subtracting pure electroweak contributions from the recent experimental value, obtained from measurements of the muon gyromagnetic ratio (g − 2), which reads 10 11 × a exp. (Hadronic) = 7 174 ± 150.Typeset with P H ys Ma T E X -precision determination of the pion form factor and calculation of the muon g − 2-