2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209467In this paper after recalling some essential tools concerning the theory of differential forms in the Cartan, Hodge and Clifford bundles over a Riemannian or Riemann-Cartan space or a Lorentzian or Riemann-Cartan spacetime we solve with details several exercises involving different grades of difficult. One of the problems is to show that a recent formula appearing in the literature for the exterior covariant derivative of the Hodge dual of the torsion 2-forms is simply wrong. We believe that the paper will be useful for students (and eventually for some experts) on applications of differential geometry on physical problems. A detailed account of the issues discussed in the paper appears in the table of contents.Some few important misprints appearing in the version of the paper published in AFLB (in a special issue dedicated to torsion) are correctedMathematical Physicstext