  An overview is presented of laser spectroscopy experiments with cold,
trapped, highly-charged ions, which will be performed at the HITRAP facility at
GSI in Darmstadt (Germany). These high-resolution measurements of ground state
hyperfine splittings will be three orders of magnitude more precise than
previous measurements. Moreover, from a comparison of measurements of the
hyperfine splittings in hydrogen- and lithium-like ions of the same isotope,
QED effects at high electromagnetic fields can be determined within a few
percent. Several candidate ions suited for these laser spectroscopy studies are
presented.
