The elements of magnetohydrodynamics (MHD) with the Hall current are presented. The governing partial differential equations are, like those of ideal MHD, quasi-linear, but unlike ideal MHD, are not hyperbolic. However, they do possess real characteristics which are shown to be associated with the sound wave and the surfaces ø(r, t) = const. determined by B. ∇ø = 0. Properties of weak and strong discontinuities are discussed, and comparisons are made with ideal MHD. It is shown that generalizations of dipole layers appear as a result of discontinuities in the magnetic field.