  We give a short outline, in Sec.\ 2, of the historical development of the
gauge idea as applied to internal ($U(1),\, SU(2),\dots$) and external
($R^4,\,SO(1,3),\dots$) symmetries and stress the fundamental importance of the
corresponding conserved currents. In Sec.\ 3, experimental results with neutron
interferometers in the gravitational field of the earth, as inter- preted by
means of the equivalence principle, can be predicted by means of the Dirac
equation in an accelerated and rotating reference frame. Using the Dirac
equation in such a non-inertial frame, we describe how in a gauge- theoretical
approach (see Table 1) the Einstein-Cartan theory, residing in a Riemann-Cartan
spacetime encompassing torsion and curvature, arises as the simplest
gravitational theory. This is set in contrast to the Einsteinian approach
yielding general relativity in a Riemannian spacetime. In Secs.\ 4 and 5 we
consider the conserved energy-momentum current of matter and gauge the
associated translation subgroup. The Einsteinian teleparallelism theory which
emerges is shown to be equivalent, for spinless matter and for
electromagnetism, to general relativity. Having successfully gauged the
translations, it is straightforward to gauge the four-dimensional affine group
$R^4 \semidirect GL(4,R)$ or its Poincar\'e subgroup $R^4\semidirect SO(1,3)$.
We briefly report on these results in Sec.\ 6 (metric-affine geometry) and in
Sec.\ 7 (metric-affine field equations (\ref{zeroth}, \ref{first},
\ref{second})). Finally, in Sec.\ 8, we collect some models, currently under
discussion, which bring life into the metric-affine gauge framework developed.

General Relativity and Quantum Cosmology;High Energy Physics - Theory