The Electron Mass and Calcium Isotope Shifts : High Precision Measurements of Bound Electron g Factors of Highly Charged Ions Introduction The g Factor Exploring Atomic Structure and Fundamental Constants Penning Trap Physics Towards the Measurement of the Larmor to cyclotron Frequency Ratio Determination of the Atomic Mass of the Electron Outlook A New Generation of High Precision Penning Trap. 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 underlying measurement principle combines a high precision measurement of the Larmor to cyclotron frequency ratio on a single hydrogen like carbon ion studied in a Penning trap with very accurate calculations of the so called bound electron g factor. Here the g factors of the valence electrons of two lithium like calcium isotopes have been measured with relative uncertainties of a few 10^{ 10} constituting an as yet unrivaled level of precision for lithium like ions. These calcium isotopes provide a unique system across the entire nuclear chart to test the pure relativistic nuclear recoil effect.