The ALPHATRAP experiment at the Max-Planck Institute for Nuclear Physics in Heidelberg aims at probing the validity of quantum electrodynamics in extremely strong electromagnetic fields. To this end, ALPHATRAP will determine the value of the magnetic moment, or the g-factor, of the electron bound in highly charged ions. Quantum electrodynamics predicts this value with extraordinary precision. As the bound electron in highly charged ions is exposed to the strongest fields available for high-precision spectroscopy in the laboratory, reaching up to 1016 V/cm in hydrogenlike lead 208Pb81+, a comparison of the theoretical prediction with a measured value can yield the most stringent test of the Standard Model in strong fields. The targeted preci...