The MATS project for research on short-lived nuclides using ion traps is described. The physical program is aimed at performing nuclear-physical and astrophysical research using exotic nuclei which are near their boundaries of nucleonic stability. The project is devoted to precision measurements of the masses (total binding energy) and spectroscopic characteristics of ideally separated nuclides in traps. The development of novel methods will also make it possible to develop the applied components of the project.