  A comprehensive account of a new structured algorithm for obtaining
nonrelativistic diffeomorphism invariances in both space and spacetime by
gauging the Galilean symmetry in a generic nonrelativistic field theoretical
model is provided.
  Various applications like the obtention of nonrelativistic diffeomorphism
invariance, the introduction of Chern-Simons term and its role in fractional
quantum Hall effect, induction of diffeomorphism in irrotational fluid model,
abstraction of Newton-Cartan geometry and the emergence of Horava-Lifshitz
gravity are discussed in details.
