Soft breaking of N=4 super-Yang-Mills theory

We discuss the problem of symmetry breaking for the maximally extended supersymmetric Yang-Mills theory. We construct various symmetry breaking terms which may break both the gauge group and the internal supersymmetry. We show that some of these terms destroy the finiteness of the quantum corrections of the unbroken theory though a restricted class do not. We finally briefly analyse various problems which would arise if we tried to apply the finite but broken theory to the known particles at present energies. (orig.)