The nature of the motion and properties of high temperature plasma in a magnetic field is of particular interest for the problem of producing controlled thermonuclear reactions. The most general theoretical approach to such problems lies in the description of the plasma by the Boltzmann and Maxwell equations that connect the self-consistent electric and magnetic fields with the ion and electron distribution functions. The exact equations for the motion of plasma in an electromagnetic field can only be solved in certain simple cases especially because the fields are influenced by the collective motion of all the particles. For a certain class of problems it is possible to work out a procedure for decreasing the number of variables and thus simplify the characteristic equations. In this work the following cases are considered and equations derived: equations for the macroscopic motion of the plasma; hydrodynamics of a low pressure plasma; instability of plasma in a magnetic field with an anisotropic ion velocity distribution; stability of a pinched cylindrical plasma using the kinetic equation; non-linear one-dimensional motion of a rarefied plasma.