Since its inception, in the beginning of the ’80s, Diffeology has become an alternative for a re-foundation of Differential Geometry. With its developments in Higher Homotopy Theory, Fiber Bundles, Cartan de Rham Calculus, Moment Maps and the new Symplectic Program, Diffeology covers a large category of traditional objects and constructions. From infinite dimensional spaces to singular quotients, Diffeology extends its scope far over