A measurement of the cross section for e +e - --> hadrons using 11 000 hadronic decays of the Z boson at ten different center-of-mass energies is presented. A three-parameter fit gives the following values for the Z mass Mz, the total width Gammaz, the product of the electronic and hadronic partial widths GammaeGammah, and the unfolded pole cross section sigma 0: MZ=91.171±0.030(stat)±0.030 (beam) GeV, GammaZ=2.511±0.065 GeV, GammaeGammah=0.148±0.006 (stat.)±0.004 (syst.) GeV 2, sigma0=41.6±0.7(stat.)±1.1 (syst.) nb, Good agreement with the predictions of the standard model is observed. From a two-parameter fit the number of massless neutrino generations is found to be Nnu = 2.97±0.26. Thus the hypothesis of a fourth neutrino with mass less than 40 GeV is excluded with 95% confidence level. Combining the cross section measurements with the ratio {Gamma l}/{Gamma h} reported in another DELPHI paper [Phys. Lett. B 241 (1990) 425], the hadronic, leptonic and invisible widths are found to be Gammah=1741±61 MeV, Gammal=85.1±2.9 MeV, {Gamma h}/{Gamma l}=20.45±0.98 , Gammainv=515±54 MeV, in good agreement with the standard model.