Abstract: This Letter describes the current most precise measurement of the W boson pair production cross section and most sensitive test of anomalous WW gamma and WWZ couplings in p (p) over bar collisions at a center-of-mass energy of 1.96 TeV. The WW candidates are reconstructed from decays containing two charged leptons and two neutrinos. Using data collected by the CDF II detector from 3: 6 fb(-1) of integrated luminosity, a total of 654 candidate events are observed with an expected background of 320 +/- 47 events. The measured cross section is sigma(p (p) over bar -> W+W- +X) = 12.1 +/- 0.9(stat)(-1.4)(+1.6)(syst) pb, which is in good agreement with the standard model prediction. The same data sample is used to place constraints on anomalous WW gamma and WWZ couplings.