2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162200We provide an exposition and proof of Renault's equivalence theorem for crossed products by locally Hausdorff, locally compact groupoids. Our approach stresses the bundle approach, concrete imprimitivity bimodules and is a preamble to a detailed treatment of the Brauer semigroup for a locally Hausdorff, locally compact groupoid.69 pages. Minor changes. Page numbering is different from published version available at http://nyjm.albany.edu:8000/m/2008/3.htmOperator Algebras46L55, 46L05text