Fundamental tests of nature and a precision measurement of the electron mass

The presentation will provide an overview on recent fundamental applications of precision measurements with cooled and stored ions in Penning traps. One the one hand, precision Penning-trap mass measurements provide indispensable information for neutrino physics and for testing fundamental symmetries. On the other hand, in-trap measurements of the bound-electron $g$-factor in highly-charged hydrogen-like ions allow for better determination of fundamental constants and for constraining Quantum Electrodynamics. Furthermore, ongoing preparations for the experimental comparison of the proton and antiproton g-factors will allow us to achieve a crucial test of the Charge-Parity-Time reversal symmetry. Among others a substantial improvement of the atomic mass of the electron by combining a very accurate measurement of the magnetic moment of a single electron bound to a carbon nucleus with a state-of-the-art calculation in the framework of bound-state Quantum Electrodynamics will be presented. The achieved precision of the atomic mass of the electron surpasses the current CODATA value by a factor of 13.