We will discuss a few mathematical problems from stellar dynamics for the evolution of stars. First, we will consider the turning point principle (TPP) for the stability of steady stars. Second，the dynamical issues (expanding, collapse, or oscillations) near stable or unstable stars will be discussed. Third, we will relate Chandrasekhar mass (the maximum mass of nonrotating white dwarf stars) to the optimal constant of a Hardy-Littlewood-Sobolev inequality. The implication of this relation to the dynamical problems will be discussed. Lastly, we will mention some open problems on this subject.
