2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79681We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.60 pages, LaTeXFunctional AnalysisMathematical Physics46F30; 26E15; 46E50; 35D05text