The common aim of the research at the Precision Frontier is to test the discrete symmetries in particle physics. This is done by placing a sensitive system (which can be a molecule, ion, atom or another particle) in a highly controlled environment, so that its properties can be very precisely measured. By comparing these precise measurements to equally precisely predicted properties, minute deviations due to new physics can be identified. In one research line we focus on the violation of Parity in trapped ions, atoms and molecules. In a second research line we focus on searches for permament Electric dipole moments (EDMs). Many extensions of the Standard Model predict the electron to have a dipole moment that is close to the current best experimental limit, making this a uniquely sensitive low-energy probe of physics beyond the Standard Model. In our electron-EDM research programme we use advanced techniques to manipulate cold molecules. To carry out and interpret this experiment, the VSI unites its theoretical and experimental expertise. Additionally, in a collaboration with the University of Mainz we investigate the EDM of the Xenon-129 atom.