gjfactor of an electron bound in a hydrogenlike ion

We present a detailed theoretical evaluation for the ${g}_{j}$ factor of a bound electron in hydrogenlike ions up to $Z=94.$ All quantum electrodynamical corrections of order $(\ensuremath{\alpha}/\ensuremath{\pi})$ are evaluated in detail and various other contributions to the ${g}_{j}$ factor are computed and listed for 61 Z. A comparison with all existing experiments is carried out and excellent agreement is found. The present uncertainty in our calculations is discussed. It is not possible to improve this precision with only minor effort since two-photon bound-state QED terms are uncalculated up to now.