Results are presented on the production of jets of particles in association with a Z/γ∗ boson, in proton-proton collisions at s√=7  TeV with the ATLAS detector. The analysis includes the full 2010 data set, collected with a low rate of multiple proton-proton collisions in the accelerator, corresponding to an integrated luminosity of 36  pb−1. Inclusive jet cross sections in Z/γ∗ events, with Z/γ∗ decaying into electron or muon pairs, are measured for jets with transverse momentum pT>30  GeV and jet rapidity |y|<4.4. The measurements are compared to next-to-leading-order perturbative QCD calculations, and to predictions from different Monte Carlo generators implementing leading-order matrix