The W + W- production cross section is measured from a data sample corresponding to a total integrated luminosity of 683 pb-1, collected by the ALEPH experiment at LEP at centre-of-mass energies from 183 to 209 GeV. Individual cross sections for the different topologies arising from W decays into leptons or hadrons, as well as the total W-pair cross section are given at eight centre-of-mass energies. The results are found to be in agreement with recently developed Standard Model calculations at the one percent level. The hadronic branching fraction of the W boson is measured to be = 67.13 0.37(stat.) 0.15(syst.)%, from which the CKM matrix element is determined to be 0.958 0.017(stat.) 0.008(syst.)