Novosibirsk: Parallel. 2015 - 300 c. The monograph describes the theoretical foundations, numerical methods and results of mathematical modeling of shock-wave and detonation processes in gas mixtures of metal particles . The original results concerning the analysis of shock-wave currents taking into account non-equilibrium processes of melting/crystallization and combustion, as well as the phenomenon of heterogeneous detonation in monodisperse and polydisperse gas mixtures. Studies cover the structure and modes of propagation of stationary waves, initiation problems, stability of stationary and non-stationary plane waves, the flow of cellular detonation, the problem of diffraction and propagation in variable geometry channels.