2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165260This 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.revised version, accepted for publication in Rev. Mod. PhysOther Condensed Mattertext