  This contribution summarises the theoretical basics for the theory of x-ray
matter interaction and is based on a quantised description of the
electromagnetic field. In view of a formally transparent presentation, we adopt
the approach of second quantisation for the electronic degrees of freedom. We
start out from the minimal coupling Hamiltonian that in principle contains all
levels of electron correlation and treat the x-ray matter interaction in lowest
order perturbation theory. We give the explicit derivation of the
photoionisation (x-ray absorption) cross section and the doubly differential
cross sections for elastic and inelastic Thomson scattering, as well as
resonant inelastic x-ray scattering. A connection to relevant experimental
techniques is attempted. At some instances, the electronic Hamiltonian is
approximated by a mean-field Hamiltonian, in order to facilitate the
interpretation of the results and connect experimental observables with the
underlying fundamental quantities of the quantum system under study.
