This book presents recent and very elementary developmentsof a theory of multiplication of distributions in the fieldof explicit and numerical solutions of systems of PDEs ofphysics (nonlinear elasticity, elastoplasticity,hydrodynamics, multifluid flows, acoustics). Theprerequisites are kept to introductory calculus level sothat the book remains accessible at the same time to puremathematicians (as a smoothand somewhat heuristicintrodcution to this theory) and to applied mathematicians,numerical engineers and theoretical physicists (as a tool totreat problems involving products of distributions).