to the physical applications of invariant wave equations -- The general theory of invariant wave equations -- The external field problem -- Mathematics of invariant wave equations -- Method of characteristics in the external field problem or How to recognize an acausal equation when you see one -- Particles with spin S ? 1 in an external field -- Nonlinear invariant wave equations -- Structure properties of solutions of classical non-linear relativistic field equations -- Relevance of classical solutions to quantum theories -- Yang mills instantons, geometrical aspects -- Quantum theory of non-linear invariant wave (field) equations or: Super selection sectors in constructive quantum field theory -- The S-operator for spin-0 and spin-particles in time-dependent external fields.