This article is the first part of a review of the theory of wave phenomena in plasmas. The basic kinetic theory is developed taking into account coulomb collisions. From this magnetohydrodynamic equations are derived. It is demonstrated that it is legitimate to deal with a closed subset of these equations either in the limit of collision-dominated phenomena, or in the limit where the effective phase velocities of the phenomena of interest are much greater than thermal speeds. In case of collision-dominated plasmas the theory of transport coefficients is discussed.These equations are then applied to an extensive treatment of small amplitude wave phenomena in plasmas. A discussion of the dissipative effects on hydromagnetic waves is given. Hydromagnetic waves are also considered from the Chew, Goldberger and Low theory. Longitudinal and transverse oscillations in current-carrying plasmas are also discussed.Oscillations of a cylindrical plasma are considered and the phenomenon of ion cyclotron resonance is discussed. The possibility of radiation by plasma oscillations by a uniform sphere is exhibited. Some general results on the stability of longitudinal electron oscillations in non-uniform plasmas are given.A brief treatment of large amplitude electron oscillations is given and the breaking of these oscillations as a dissipative mechanism for the organized plasma motion is discussed.Part II of this paper, to appear in a future issue of this journal, will be devoted to the discussion of plasma oscillations directly from the kinetic theory.