  The Maxwell algebra is the result of enlarging the Poincar\'{e} algebra by
six additional tensorial Abelian generators that make the fourmomenta
non-commutative. We present a local gauge theory based on the Maxwell algebra
with vierbein, spin connection and six additional geometric Abelian gauge
fields. We apply this geometric framework to the construction of Maxwell
gravity, which is described by the Einstein action plus a generalized
cosmological term. We mention a Friedman-Robertson-Walker cosmological
approximation to the Maxwell gravity field equations, with two scalar fields
obtained from the additional gauge fields. Finally, we outline further
developments of the Maxwell symmetries framework.
