  We show how the Newton-Cartan formulation of Newtonian gravity can be
obtained from gauging the Bargmann algebra, i.e., the centrally extended
Galilean algebra. In this gauging procedure several curvature constraints are
imposed. These convert the spatial (time) translational symmetries of the
algebra into spatial (time) general coordinate transformations, and make the
spin connection gauge fields dependent. In addition we require two independent
Vielbein postulates for the temporal and spatial directions. In the final step
we impose an additional curvature constraint to establish the connection with
(on-shell) Newton-Cartan theory. We discuss a few extensions of our work that
are relevant in the context of the AdS-CFT correspondence.
