This thesis presents the first measurement of the $\\ww$ production cross section in proton-proton collisions\nat $\\sqrt{s} = 7 \\TeV$ using the complete data set of $4.7 \\ifb$ collected by the ATLAS detector at the LHC in the year 2011.\nThree di-leptonic decay channels of the $\\ww$ pairs are used for this analysis: decays into two electrons,\ntwo muons, and decays into one electron and one muon. For each channel, a region with a high fraction of $\\ww$ events is selected and\ncontributions from background processes are estimated using Monte Carlo simulations and data-driven techniques.\nIn total, 1524 $\\ww$ candidate events are selected, with an estimated background of \\mbox{$545 \\pm 52$ events}.\nThe result of the measurement is: $$\\sigma (pp \\rightarrow \\ww) = 52.6 \\pm 2.1 \\text{(stat)} \\pm 4.5 \\text{(syst)} \\pm 2.1 \\text{(lumi)} \\pb$$ This is compatible with the Standard Model cross-section prediction at next-to-leading order of $\\sigma (pp \\rightarrow \\ww) = 47.0^{+2.0}_{-1.5}$ pb.