  In Einstein's gravitational theory, the spacetime is Riemannian, that is, it
has vanishing torsion and vanishing nonmetricity (covariant derivative of the
metric). In the gauging of the general affine group ${A}(4,R)$ and of its
subgroup ${GL}(4,R)$ in four dimensions, energy--momentum and hypermomentum
currents of matter are canonically coupled to the one--form basis and to the
connection of a metric--affine spacetime with nonvanishing torsion and
nonmetricity, respectively. Fermionic matter can be described in this framework
by half--integer representations of the $\overline{SL}(4,R)$ covering subgroup.
--- We set up a (first--order) Lagrangian formalism and build up the
corresponding Noether machinery. For an arbitrary gauge Lagrangian, the three
gauge field equations come out in a suggestive Yang-Mills like form. The
conservation--type differential identities for energy--momentum and
hypermomentum and the corresponding complexes and superpotentials are derived.
Limiting cases such as the Einstein--Cartan theory are discussed. In particular
we show, how the ${A}(4,R)$ may ``break down'' to the Poincar\'e (inhomogeneous
Lorentz) group. In this context, we present explicit models for a symmetry
breakdown in the cases of the Weyl (or homothetic) group, the ${SL}(4,R)$, or
the ${GL}(4,R)$.
