White dwarfs are compact objects that stand against gravitational collapse by their internal pressure of degenerate matter. In this work we aimed to perform an introductory study on these stars, using two equations of state: (I) an ideal Fermi gas and (II) the one by Baym Pethick and Sutherland (BPS). In addition, we analyzed these two state equations in two scenarios, the Newtonian and the one from General Relativity, which allowed us to analyze the effects of curved space-time. We also studied a rotating white dwarf, finding a metric for this case. With these two cases, with rotation and static well determined, we introduced the concepts of instability by the turning point criterion and dynamic instability criterion. Finally, with the RNS program, we performed the numerical resolution of the BPS equation of state with ($J=constant$ and $J=0$ respectively) rotation in order to analyze the behavior of the turning point criterion in these two cases. All the numerical resolution of the equations of a non-rotating white dwarf were made using FORTRAN programs written by the author and all the results found were compatible with those of the literature.