  We present results on the production of jets of particles in association with
a $Z/\gamma^*$ boson, in proton-proton collisions at $\sqrt{s} = 7$ TeV with
the ATLAS detector at the LHC. 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 $36 \rm pb^{-1}$.
Inclusive jet cross sections in $Z/\gamma^*$ events, with $Z/\gamma^*$ decaying
into electron or muon pairs, are measured for jets with transverse momentum
$p_T >$ 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 elements
supplemented by parton showers.
