In this thesis, quantum electrodynamic (QED) effects in few-electron highly charged ions are investigated. The interaction of the electron with the nucleus is taken into account in a nonperturbative manner. A versatile approach to accurately calculate self-energy corrections combining finite basis sets with analytical methods is presented. The approach is applicable to many-electron ions using the screening-potential approximation. The method is applied to calculate self-energy corrections to the energy level of the electron in the 4d3∕2 state of ¹³¹Xe¹⁷⁺ and to the excitation energy of the 4d → 4f excitation in ¹⁸⁷Re²⁹⁺. QED corrections to the g factor of lithiumlike and boronlike ions in a wide range of nuclear charges are presented. Many-electron contributions as well as radiative effects on the one-loop level are calculated. Contributions resulting from the interelectronic interaction, derived in a QED framework, and most of the terms of the vacuum polarization effect are evaluated to all orders in the nuclear coupling strength Zα. Uncertainties resulting from nuclear size effects, numerical calculations, and uncalculated effects are discussed. Finally, a new approach to determine the fine-structure constant α using a weighted difference of the bound-electron g factor and energy in hydrogenlike systems is put forward. It is shown that nuclear structural effects are sufficiently well suppressed while sensitivity to α is enhanced in this weighted difference, as compared to the g factor
