  We provide a new formulation of nonrelativistic diffeomorphism invariance. It
is generated by localising the usual global Galilean Symmetry. The
correspondence with the type of diffeomorphism invariant models currently in
vogue in the theory of fractional quantum Hall effect has been discussed. Our
construction is shown to open up a general approach of model building in
theoretical condensed matter physics. Also, this formulation has the capacity
of obtaining Newton - Cartan geometry from the gauge procedure.
