The MATS project (Measurements with an Advanced Trapping System) is concerned with trapping unstable nuclei in three-dimensional trap systems. This allows for the measurement of the masses of these nuclei, one of the most basic nuclear properties. This approach is already possible with only few, or only single trapped atomic nuclei. In addition, such traps allow for the measurement of magnetic moments of nuclei, which give direct insight into their structure. It is also possible to perform high-precision decay-spectroscopy on nuclei which are stored in such traps.