The main topic of my PhD Thesis is related to nuclear structure studies of neutron-rich nuclei following the beta-decay of 34Mg isotopes produced at the ISOLDE facility of CERN and measured using one of the newest permanent experimental setups, the ISOLDE Decay Station (IDS). I will also describe this setup and some of developments I contributed to during the three years spent as a PhD Student at CERN. This Thesis is divided into 6 chapters: The first chapter contains a description of the radioactive ion-beam production techniques with an emphasis on the ISOL technique and an overview of the capabilities of the ISOLDE facility of CERN. The second chapter is dedicated to the IDS setup, its capabilities and development since the first experimental campaign in 2014. The GEANT4 simulations of IDS are the subject in the third chapter, which cover mainly the HPGe detectors, the core detection system of IDS, and a possible improvement related to reducing the large background present in the high energy region of the HPGe detectors. In the fourth chapter some theoretical aspects will be discussed related to shape coexistence in nuclei with an emphasis on the N=20 “Island of Inversion” together with the physical motivation for studying the 34Al and 34Si isotopes. The fifth chapter presents the experimental setup and results from the IS530 experiment at ISOLDE, CERN, during which the beta-decay of 34Mg was studied. The interpretation of the experimental results and a comparison with state-of-the-art shell-model calculations will be discussed in the sixth chapter followed by conclusions and outlook