  This article reviews recent experimental and theoretical progress on
many-body phenomena in dilute, ultracold gases. Its focus are effects beyond
standard weak-coupling descriptions, like the Mott-Hubbard-transition in
optical lattices, strongly interacting gases in one and two dimensions or
lowest Landau level physics in quasi two-dimensional gases in fast rotation.
Strong correlations in fermionic gases are discussed in optical lattices or
near Feshbach resonances in the BCS-BEC crossover.
