This monograph examines multidimensional stability of strong discontinuities (e.g. shock waves) for systems of conservation laws and surveys the author's results for models of ideal magnetohydrodynamics (classical, 'pressure anisotropic', relativistic) and electrohydrodynamics. The primary attention is concentrated on linearised stability analysis, especially on the issue of uniform stability in the sense of the uniform Kreiss-Lopatinski condition. A so-called 'equational' approach based on obtaining, by the dissipative integrals technique, a priori estimates without loss of smoothness for...