In the book, two types of instabilities, namely Rayleigh ¿ Taylor (RT) instability and resistive instability, have been studied. A frequency band has been found for the first time for the existence of RT instability in the Hall Thruster plasma having finite temperature ions. Then the role of ionization and different profiles of the density and electron drift velocity has been clarified to the evolution of RT instability. It has been shown that the growth rate of this instability is not so sensitive to the velocity profile but the perturbed potential varies significantly for different profiles of the electron drift velocity. In the next part of the thesis, two types of resistive instabilities, namely electrostatic resistive instability and electromagnetic resistive instability, have been investigated.