2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67763We review the basic definition of a stack and apply it to the topological and smooth settings. We then address two subtleties of the theory: the correct definition of a ``stack over a stack'' and the distinction between small stacks (which are algebraic objects) and large stacks (which are generalized spaces).Differential GeometryMathematical PhysicsK-Theory and Homology22A22; 58A03, 58H05, 14A20text