From evolved Long-Period-Variable stars to the evolution of M31

One of the ways to understand the genesis and evolution of the universe is to know how galaxies have formed and evolved. In this regard, the study of star formation history (SFH) plays an important role in the accurate understanding of galaxies. In this paper, we used long-period variable stars (LPVs) for estimating the SFH in the Andromeda galaxy (M31). These cool stars reach their peak luminosity in the final stage of their evolution also their birth mass is directly related to their luminosity. Therefore, using stellar evolution models, we construct the mass function and hence the star formation history.