A PhD thesis titled  Shell Model Study for the Structure of Exotic Mg Isotopes was defended at College of Science, Department of physics on )May 11, 2023), for the PhD Candidate Mohammed Yahya Hadi. The primary aim of this study is to introduce novel theoretical data regarding the nuclear structure, focusing on regions where the model space selection exhibits considerable accuracy. The calculations involve the prediction of the positive and negative parity states, along with the calculation of reduced transition probabilities for exotic isotopes of magnesium.