2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59604We extend the notion of connection in order to be able to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of connection. Using connections, we are able to define holonomy of the orbit foliation of a Lie algebroid and prove a stability theorem. We also introduce secondary or exotic characteristic classes that generalize the modular class of a Lie algebroid.Several typos corrected. References added. Final version for publicationDifferential GeometrySymplectic Geometry53C05; 53c29; 53d17text