This thesis presents a preliminary investigation into the dynamics of a single bubble rising in a Newtonian fluid, with particular emphasis on how the bubble shape is affected by different system parameters. The analysis is carried out in terms of dimensionless numbers to ensure generality. A range of Reynolds and Eötvös numbers is explored in order to identify the various hydrodynamic regimes and to classify the corresponding bubble morphologies. The simulations are performed with the open-source solver Basilisk, which employs adaptive mesh refinement based on a quadtree data structure and a geometrical Volume-of-Fluid (VOF) method for interface reconstruction and tracking. The results show that variations in the relative magnitude of inertial, viscous, and surface-tension forces lead to substantially different bubble behaviours, whose main features are analyzed in detail.