In connection with recent x-ray spectroscopic measurements on muonic atoms, the nuclear quadrupole moment of Re-185 and Re-187 is extracted. Furthermore, new methods for the calculation of higher-order corrections for the hyperfine structure are presented, including a complete calculation of the second-order hyperfine structure and leading-order vacuum polarization corrections for extended electric quadrupole distributions inside the nucleus. QED corrections, hyperfine interactions, and the interaction with atomic electrons were evaluated and finite nuclear size effects were incorporated non-perturbatively. Here, precise calculations for transition energies and probabilities are presented, using state-of-the-art numerical methods. The first part is concerned with the structure of bound states between a muon and an atomic nucleus, so-called muonic atoms. In this thesis, several aspects of nuclear structure effects and corrections from quantum electrodynamics (QED) in the spectra of hydrogen-like systems are investigated. This article summarizes an overview talk that was concerned primarily with a selection of topics from a very rich field, in particular such that were not covered otherwise at this conference.
At the same time while providing important information on physics beyond the Standard Model, new technology such as precise clocks is developed along with the experiments motivated by fundamental physics questions. There is at present a some 4 standard deviations discrepancy between theory and experiment for the muon magnetic anomaly. Electric Dipole Moments (EDMs) may provide clues to explain the matter-antimatter asymmetry in the universe. Atomic parity violation was not only essential in the past to verify the Standard Model, still today it has a potential to find Z' bosons, leptoquarks or dark matter. Examples are dedicated searches for violations of the C, P, CP and CPT as well as of Lorentz Invariance using matter and anti-matter. High precision experiments at low energies on discrete and continuous symmetries offer the possibility to search for New Physics beyond the Standard Model. Neutron-rich $^$ intruder ground state configuration. The magnetic dipole moments and changes in mean-square charge radii of the
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