A generalised linear response theory is used to derive the dielectric function
at arbitrary wave numbers k and frequencies
w for interacting quantum systems. The connection to
thermodynamic Green functions allows the systematic perturbative treatment
going beyond RPA and treating local field corrections as well as the inclusion
of collisions on the same footing. Emphasis will be on the demonstration of
the formalism. Results will be presented for the three-dimensional as well as
two-dimensional case of an interacting electron gas. In the long-wavelength
limit, a Drude-type expression with frequency dependent relaxation time is
given bridging the theories of dielectric function and electrical
conductivity.