The plasma oscillations of a high-temperature and a degenerate plasma, both with and without an applied magnetic field, are discussed using a Green function technique. For the high-temperature plasma in lowest order the results reduce to those obtained via the linearized BoltzmannVlasov equation in the classical limit. The quantum mechanical effects are important for strong fields where the quantization of the orbits of the electrons in the field must be taken into account. The dispersion relation of a degenerate plasma in a magnetic field is obtained within the random phase approximation. This dispersion relation is discussed for various special cases. The fluctuation spectrum of the plasma is obtained by making use of the fluctuation dissipation theorem. (auth)