In this course of lectures I intend to describe Hodge theory for Thom-Mather stratified varieties (``pseudomanifolds''). The main novelty will be the treatment of the generalized inverse of , for appropriate degenerate metrics, and the corresponding Hodge decomposition. This leads to an identification of Hodge cohomology with cohomology (`Hodge theorem') and hence duality with intersection homology (`de Rham theorem'). I intend to approach the subject from the `analytic' end and progress toward the topological.