The proceedings of the conference on Exotic Nuclei and Atomic Masses (ENAM98) are the scientific contributions to the most recent meeting in a long series that dates back to the late 1950s. The conference is held every three years and the participants produce a complete review of the fields of exotic nuclei; atomic masses, moments and radii of nuclei; fission, synthesis of heavy elements, the role of radioactive nuclei in the cosmos, fundamental studies and use of radioactive ion beams. The proceedings provide an excellent overview and an up to date summary of recent developments in a field that is undergoing a rapid growth due to the advent of radioactive ion beams.