Measurement of the cross section for W boson production in association with jets in pˉp collisions at √s=1.96 TeV. The analysis uses 320 pb−1 of data collected with the CDF II detector. W bosons are identified in their eν decay channel and jets are reconstructed using an R<0.4 cone algorithm. For each W+≥ n-jet sample (where n = 1--4) a measurement of dσ(pˉp→W+≥ n jet)/dET(nth-jet) × BR(W→eν) is made, where dET(nth-jet) is the Et of the nth-highest Et jet above 20 GeV. A measurement of the total cross section, σ(pˉp→W+≥ n-jet) × BR(W→eν) with ET(nth−jet)>25 GeV is also made. Both measurements are made for jets with |η|<2 and for a limited region of the W→eν decay phase space; |ηe|<1.1, peT>20 GeV, pνT>30 GeV and MT>20 GeV. The cross sections are corrected for all detector effects and can be directly compared to particle level W + jet(s) predictions. These measurements can be used to test and tune QCD predictions for the number of jets in and kinematics of W + jets events.