In this thesis the parallel and perpendicular propagation of electrostatic waves in a magnetized plasma is investigated in the context of nonextensive q-distribution of Tsallis statistics. Logically, the properties of the electrostatic waves in a nonextensive plasma are significantly modified in comparison with that of discussed in the Maxwellian plasmas, because of the system under consideration is essentially a plasma system in a nonequilibrium stationary state with inhomogeneous temperature. For the parallel propagation the generalized dispersion relations and Landau damping of electron plasma waves and ion acoustic waves are expressed as functions of q-parameter, which quantifies the degree of nonextensivity of the system. It is shown that by decreasing the nonextensivity index q which corresponds to a plasma with excess superthermal particles, the frequency, phase velocity and group velocity of electron plasma waves and also ion acoustic waves increase. In particular, the increased numbers of superthermal particles and law velocity particles can respectively explain the strengthened and weakened modes of Landau damping for electron plasma and ion acoustic waves. Furthermore, stimulated Raman scattering in a nonextensive plasma is analytically and numerically studied and generalized wavenumbers and growth rates in both backward and forward scattering are derived in terms of q-parameter. For perpendicular propagation the dispersion relation of Bernestein waves is derived in nonextensive plasmas. It is shown that the generalized dispersion relation significantly depends on the q-parameter. The reduced number of superthermal particles shifts the Bernstein wave curves to higher wavenumbers. For harmonics whose frequency lies above the upper hybrid frequency, an increase in the value of q increases the maximum frequency and the wavenumber at which the group velocity vanishes. For Bernstein waves which propagate at frequencies lower than the upper hybrid frequency or close to it, diminishing q, or increasing the number of superthermal particles, gives rise to faster frequency falloff. The generalized electron Bernstein waves are studied in both the strongly and weakly magnetized regimes and for both small and large wavenumbers compared with the Larmor radius. It is found that for the weak magnetic field, the frequency range occupied by the mode spans the complete intraharmonic frequency, and the q value significantly affects the dispersion curves. On the other hand, in strongly magnetized regimes the frequency variation domain is extremely restricted and has little dependence on the q value.