Astrophysical gases are characterized by their macro variables, which describe the radiation field and the particle field. Radiation can be described by its frequency-dependent energy density or photon number density. Both these quantities can be integrated over frequency, yielding total radiative energy density and/or photon number density. Particles are described by their number and/or mass densities, thermal motions, partial pressures, and the charge density of ions and free electrons. Ion number densities depend on the abundances of elements in the gas and their ionization fractions. In this chapter, we describe the formalisms of the quantities describing the radiation and particle fields in astrophysical gases. We describe the cosmic ultraviolet ionizing background and starburst galaxies ionizing spectra. The principles of particle density and charge density conservation are derived, and the equation of state is presented. This chapter provides the fundamental formalism for studying the micro processes of ionization and the detailed balancing of partially ionized astrophysical gases key to modeling the ionization balance of these gases.