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Summarizing basic facts from abstract topological modules over Colombeaugeneralized complex numbers we discuss duality of Colombeau algebras. Inparticular, we focus on generalized delta functionals and operator kernels aselements of dual spaces. A large class of examples is provided bypseudodifferential operators acting on Colombeau algebras. By a refinement ofsymbol calculus we review a new characterization of the wave front set forgeneralized functions with applications to microlocal analysis.

On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets