  The complexity of quantum many-body systems originates from the interplay of
strong interactions, quantum statistics, and the large number of
quantum-mechanical degrees of freedom. Probing these systems on a microscopic
level with single-site resolution offers important insights. Here we report
site-resolved imaging of two-component fermionic Mott insulators, metals, and
band insulators using ultracold atoms in a square lattice. For strong repulsive
interactions we observe two-dimensional Mott insulators containing over 400
atoms. For intermediate interactions, we observe a coexistence of phases. From
comparison to theory we find trap-averaged entropies per particle of
$1.0\,k_{\mathrm{B}}$. In the band-insulator we find local entropies as low as
$0.5\,k_{\mathrm{B}}$. Access to local observables will aid the understanding
of fermionic many-body systems in regimes inaccessible by modern theoretical
methods.
