  An introduction to the Zwanzig-Mori-G\"{o}tze-W\"{o}lfle memory function
formalism (or generalized Drude formalism) is presented. This formalism is used
extensively in analyzing the experimentally obtained optical conductivity of
strongly correlated systems like cuprates and Iron based superconductors etc.
For a broader perspective both the generalised Langevin equation approach and
the projection operator approach for the memory function formalism are given.
The G\"{o}tze-W\"{o}lfle perturbative expansion of memory function is presented
and its application to the computation of the dynamical conductivity of metals
is also reviewd. This review of the formalism contains all the mathematical
details for pedagogical purposes.
