HITRAP is a planned ion trap facility for capturing and cooling of highly charged ions produced at GSI in the heavy-ion complex of the UNILAC-SIS accelerators and the ESR storage ring. In this facility heavy highly charged ions up to uranium will be available as bare nuclei, hydrogen-like ions or few-electron systems at low temperatures. The trap for receiving and studying these ions is designed for operation at extremely high vacuum by cooling to cryogenic temperatures. The stored highly charged ions can be investigated in the trap itself or can be extracted from the trap at energies up to about 10 keV/q. The proposed physics experiments are collision studies with highly charged ions at well-defined low energies (eV/u), high-accuracy measurements to determine the g-factor of the electron bound in a hydrogen-like heavy ion and the atomic binding energies of few-electron systems, laser spectroscopy of HFS transitions and X-ray spectroscopy.