A measurement of the W boson pair production cross section in proton-proton collisions at $\sqrt{s} = 8$  TeV is presented. The data collected with the CMS detector at the LHC correspond to an integrated luminosity of 19.4 $,\text {fb}^\text {-1}$ . The ${{\mathrm{W} }^{+} }\mathrm{W}^{-} $ candidates are selected from events with two charged leptons, electrons or muons, and large missing transverse energy. The measured ${{\mathrm{W} }^{+} }\mathrm{W}^{-} $ cross section is $60.1\pm 0.9,\text {(stat)} \pm 3.2,\text {(exp)} \pm 3.1,\text {(theo)} \pm 1.6,\text {(lumi)} \text {,pb} = 60.1\pm 4.8\text {,pb} $ , consistent with the standard model prediction. The ${{\mathrm{W} }^{+} }\mathrm{W}^{-} $ cross sections are also measured in two different fiducial phase space regions. The normalized differential cross section is measured as a function of kinematic variables of the final-state charged leptons and compared with several perturbative QCD predictions. Limits on anomalous gauge couplings associated with dimension-six operators are also given in the framework of an effective field theory. The corresponding 95 % confidence level intervals are $-5.7< c_{\mathrm {WWW}}/\Lambda ^2 < 5.9,\mathrm{TeV}^{-2}$ , $-11.4< c_{\mathrm {W}}/\Lambda ^2 < 5.4,\mathrm{TeV}^{-2}$ , $-29.2< c_{\mathrm {B}}/\Lambda ^2 < 23.9,\mathrm{TeV}^{-2}$ , in the HISZ basis.