  The Poincar\'e (inhomogeneous Lorentz) group underlies special relativity. In
these lectures a consistent formalism is developed allowing an appropriate
gauging of the Poincar\'e group. The physical laws are formulated in terms of
points, orthonormal tetrad frames, and components of the matter fields with
respect to these frames. The laws are postulated to be gauge invariant under
local Poincar\'e transformations. This implies the existence of 4 translational
gauge potentials ${e}^\alpha$ (``gravitons") and 6 Lorentz gauge potentials
${\Gamma}^{\alpha\beta}$ (``rotons") and the coupling of the momentum current
and the spin current of matter to these potentials, respectively. In this way
one is led to a Riemann-Cartan spacetime carrying torsion and curvature, richer
in structure than the spacetime of general relativity. The Riemann-Cartan
spacetime is controlled by the two general gauge field equations (3.44) and
(3.45), in which material momentum and spin act as sources. The general
framework of the theory is summarized in a table in Section 3.6. -- Options for
picking a gauge field lagrangian are discussed (teleparallelism, ECSK). We
propose a lagrangian quadratic in torsion and curvature governing the
propagation of gravitons and rotons. A suppression of the rotons leads back to
general relativity.
