Nonlinear Diffusion Problems : Lectures given at the 2nd 1985 Session of the Centro Internazionale Matermatico Estivo (C.I.M.E.) held at Montecatini Terme Italy June 10 – June 18 1985 The porous medium equation Qualitative methods for nonlinear diffusion equations Reaction diffusion problems in chemical engineering Rearrangements of functions and partial differential equations.