When ultraviolet light or soft x-ray radiation is used to illuminate a gas, it is possible for light particles (photons) to be absorbed by atoms, resulting in the emission of electrons (photoelectrons). This process is termed photoionization. It can be used to probe the electron structure of atoms and the interactions among the various atomic electrons. Here the theory of these interactions will be investigated, especially for electrons lying deep within the atom. One problem to be studied is core relaxation, the rearrangement of the remaining electrons in the atom after the departure of the photoelectron. Another problem is core polarization, the change in the arrangement of the remaining electrons in the presence of the departing photoelectron.