This thesis investigates the inclusive production cross section of W and Z bosons as well as their ratio in association with one jet. The cross sections are estimated with 7 TeV LHC proton-proton collision data, collected by ATLAS during 2010, resulting in an integrated luminosity of approximately 40 pb−1. This thesis focuses on the analysis performed in the electron channel, while comparisons with the results obtained in the muon channel also are included. This is the first time the W and Z production cross sections are measured at this center-of-mass energy and the results are important for various reasons, such as testing perturbative theoretical calculations and understanding these signatures as backgrounds to other physics processes. The final inclusive cross section values obtained in the electron channel are the following: -σ(W → eν ) = 10.255 ± 0.031(stat) ± 0.190(syst) ± 0.349(lumi) ± 0.156(acc) nb -σ(Z → ee) = 0.952 ± 0.010(stat) ± 0.026(syst) ± 0.032(lumi) ± 0.019(acc) nb. The results agree well with NNLO Standard Model predictions within the uncertainties of the measurement. In addition, the measurement of σ(W + 1jet)/σ(Z + 1jet) as a function of cumulative jet pT is presented for the first time. This measurement has the advantage of partial and full cancellations of various uncertainties, which are parametrized in the equivalent pT distribution. The results are found to be compatible within uncertainties with perturbative LO and NLO QCD predictions.