Paper I. Mattias Lennartsson, “Residues and currents from singular forms on complex manifolds”, preprint. Paper II. Mats Andersson, Richard Lärkäng, Mattias Lennartsson and Håkan Samuelsson Kalm, “The ∂-equation for (p, q)- forms on a non-reduced analytic space”, preprint. Paper III. Mattias Lennartsson, “Residues of singular differential forms on complex submanifolds”, preprint