The production of W boson pairs in proton-proton collisions at √s=8 TeV 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 WW 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 WW production cross section, which is found to be 71.1 ± 1.1(stat) − 5.0+ 5.7(syst) ± 1.4(lumi) pb. This agrees with the next-to-next-to-leading-order Standard Model prediction of 63. 2− 1.4+ 1.6(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.