Exploring and understanding the lives and deaths of stars are fundamental goals of astronomical research. Stars in the late stages of stellar evolution are of particularly interest as they are major sites for nucleosynthesis, where the processed material later returned to the cosmic matter cycle is produced. Massive stars are the main contributors of heavy elements through supernova explosions, but low-to-intermediate-mass giants are believed to be responsible for at least one third of all the carbon produced, a significant fraction of the heavier s-process elements as well as (possibly?) a significant amount of cosmic dust. Such stars are also (maybe?) progenitors to type 1A supernovae. It is of great importance to not only observe but also describe these cool giants with realistic models based on first principle. In this seminar I will present the main results from my PhD thesis, where I theoretically explore the dynamics and mass-loss mechanism of low-to-intermediate mass stars on the Asymptotic Giant Branch (AGB).