Stellar evolution models are fundamental to modern astrophysics, providing critical insights into the life cycles of stars, the ages of star clusters and galaxies, nucleosynthesis, cosmic chemical evolution, and the prediction of phenomena such as supernovae and gravitational waves. However, these models are sensitive to uncertainties in mass-loss rates, particularly during late evolutionary phases including the asymptotic giant branch (AGB), during which the stellar evolution is driven by the star’s decreasing mass. We thus suffer significant challenges in modelling AGB stars due to the poorly constrained mass-loss rates, which critically influence the duration of the thermally pulsing phase. In this thesis, we focus on improving the modelling of AGB stars using the open-source stellar evolution code MESA. This allows us, and future researchers, to better constrain the dependence of thermal pulse properties on the variable stellar mass, which in turn is essential to constrain the contribution of AGB stars to galactic chemical evolution.

This thesis also investigates the impact of mass changes due to binary mass transfer, another scenario in which the stellar evolution is profoundly affected. By computing stellar evolution models with varying core mass fractions, we aim to better understand post-mass-transfer stellar evolution and contribute to the development of interpolation tables for use in rapid population synthesis codes. These models aim to enhance the accuracy of simulations involving binary and higher-order stellar systems. Understanding stars with variable mass is critical to accurately model their evolutionary paths and their broader astrophysical significance. This thesis not only improves our ability to model AGB stars but also enhances our understanding of how mass variability,

whether from stellar winds or binary interactions, shapes stellar evolution. These insights are essential for refining predictions about galactic chemical enrichment and the complexities of interacting stellar populations, thereby advancing our overall knowledge of stellar populations across the Universe