A review of the fundamental problem of galactic dynamics

The dynamics of stellars systems is fully specified by its distribution function - the phase density of its consistuent stars - and the form of the gravitational potential that binds it together. The so-called fundamental problem of galactic dynamics is the recovery of this information from the observable properties of a galaxy. I will review past results concerning this problem in the spherical and axisymmetric geometry. Finally I will show my own contribution to the problem for the case of infinitely thin axisymmetric stellar systems.