In order to obtain information about the properties of a given system, it is necessary to perturb it and study its response to different perturbations. The response of a system may be described by generalized susceptibilities associated with different quantities and different probes. Here we consider a detailed quantum description of the effect of a space- and time-dependent perturbation on the state of a system. Considering small perturbations, the linear response is considered and expressions for the susceptibilities are obtained. These satisfy general properties, associated with causality considerations. These imply the so-called Kramers-Kronig relations. One example of a susceptibility is a magnetic or electric susceptibility, in response to a magnetic or electric external field. An important quantity is the dynamical structure factor that provides information on charge or spin density distributions on a given material and that may be probed by incident radiation of different forms. Another example of a response function is the conductivity, whose expression in linear theory provides a realization of the Kubo formulas for the response functions. A discussion of dissipation effects and the fluctuation-dissipation theorem is presented.