The production of W boson pairs in proton-proton collisions at root s = 8TeV is studied using data corresponding to 20.3 fb(-1) of integrated luminosity collected by the ATLAS detector during 2012 at the CERN Large Hadron Collider. The W bosons are reconstructed using their leptonic decays into electrons or muons and neutrinos. Events with reconstructed jets are not included in the candidate event sample. A total of 6636 W W candidate events are observed. Measurements are performed in fiducial regions closely approximating the detector acceptance. The integrated measurement is corrected for all acceptance effects and for the W branching fractions to leptons in order to obtain the total W W production cross section, which is found to be 71.1 +/- 1.1( stat) + (5.7) (5.0) (syst) +/- 1 : 4( lumi) pb. This agrees with the next-to-next-to-leading-order Standard Model prediction of 63.2(+1.6) (-1.4) (scale) +/- 1.2(PDF) pb. Fiducial differential cross sections are measured as a function of each of six kinematic variables. The distribution of the transverse momentum of the leading lepton is used to set limits on anomalous triple-gauge-boson couplings.