2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228676The Dixmier-Douady invariant is the primary tool in the classification of continuous trace $C^*$-algebras. This expository note explores its properties from the perspective of classical algebraic topology.Typos corrected, very minor changes. This paper has been accepted by the Notices AMS and will appear as a feature article - projected for August 2009Operator AlgebrasAlgebraic Topology46L05; 55N05 (Primary) 46L20, 46L85;55-02 (Secondary)text