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One of the major challenges of contemporary nuclear structure research is understanding the internal structure of nuclei with exotic neutron-proton ratios and interpreting the various phenomena associated with their underlying nucleon configurations. Fundamentally, the structure and hence, the shape of these nuclei is governed by the interplay of macroscopic and microscopic shell effects. Consequently, investigations associated with the influence of the various shape degrees of freedom on the collective and single-particle excitation properties remain a central theme of current research efforts. My research to date has focused on investigating the nature of these excitations, particularly looking at the interplay of collective and single-particle degrees of freedom, the evolution of collectivity and accompanying shape-phase transitions/coexistence, as well as searching for evidence of stable asymmetric shapes in neutron-rich nuclei with extreme isospin ratios. The primary objective is to construct a comprehensive understanding of the physical structure arising from these excitations from the measured ground- and excited-state properties and develop a coherent description of the nuclear system, in general. This work is accomplished mostly by using several in-beam gamma-ray spectroscopic techniques such as Coulomb excitation, fusion-evaporation, and deep in-elastic reactions, and lifetime measurements to probe the underlying structure.