This thesis presents the first isotope-shift measurement of bound-electron g-factors of highly charged ions and determines the most precise value of the electron mass in atomic mass units, which exceeds the value in the literature by a factor of 13. As the lightest fundamental massive particle, the electron is one of nature's few central building blocks. A precise knowledge of its intrinsic properties, such as its mass, is mandatory for the most accurate tests in physics - the Quantum Electrodynamics tests that describe one of the four established fundamental interactions in the universe. The...