Matter and radiation exchange momentum via radiative force, and exchange energy via radiative heating and cooling. The radiative force generally pushes a material to lift up or move it against, e.g., gravity, and affects the dynamics of matter. The radiative heating and cooling also change the structure and dynamics of gaseous astronomical objects. Matter, whose dynamical and thermal states are changed, would also affect radiation at the same time. The method to simultaneously treat matter and radiation is radiation hydrodynamics. Radiation hydrodynamics is important in many astrophysical situations; in the cool low energy regime such as an interstellar gas, in the intermediate regime like stellar and planetary atmospheres, and in the hot high energy regime around, e.g., black hole environments and at the early universe. In this chapter, using the results of Part I and Chap. 22 , we couple the basic equations for matter and radiation step by step. In addition, we briefly discuss several stages of approximations and classification by the strength of coupling between matter and radiation.