Besides the possibilities of the magnetic fusion those of inertial fusion have increasingly found interest. Bundled photon and corpuscular beams shall be symetrically focussed from the outside on a pellet with the fusion fuel being compressed far beyond the density of the ordinary solids. Laser, light ion and heavy ion beams can be used as driver beams. The GSI took over the project leadership for a five years' research programme with formulated questions on heavy ion fusion. The project is promoted by the BMFT. During the international symposium the opportunity of intensive discussions on research work in this field in different countries was made use of.