  We report an ab initio calculation of the shielding of the nuclear magnetic
moment by the bound electron in hydrogen-like ions. This investigation takes
into account several effects that have not been calculated before (electron
self-energy, vacuum polarization, nuclear magnetization distribution), thus
bringing the theory to the point where further progress is impeded by the
uncertainty due to nuclear-structure effects. The QED corrections are
calculated to all orders in the nuclear binding strength parameter and,
independently, to the leading order in the expansion in this parameter. The
results obtained lay the ground for the high-precision determination of nuclear
magnetic dipole moments from measurements of the g-factor of hydrogen-like
ions.
