  This thesis deals with the construction of an eleven-dimensional gauge
theory, off-shell invariant, for the M Algebra. The theory is built using a
Transgression Form as a Lagrangian.
  In order to accomplish this, one must first analyze the general construction
of Transgression Gauge Field Theories, for an arbitrary symmetry group (Chapter
3). Some interesting results regarding this point are (1) the calculation of
Noether Charges which are off-shell conserved, (2) the association of the
double connection structure of the Transgression Form with both orientations of
the basis manifold and (3) the Subspace Separation Method, which allows us to
divide the action in bulk and boundary terms, and to split them in terms which
reflect the physics corresponding to a symmetry group choice.
  To construct the gauge theory explicitly, it is necessary to buid a new
mathematical tool, called S-Expansion procedure. Analyzing the M Algebra under
the light of this method, it is possible to construct an invariant tensor for
it. This method is developed in a general way and, given a Lie algebra and an
Abelian, finite semigroup, it allows us to generate new Lie algebras
(S-Expanded Algebras, Resonant Subalgebras, Resonant Forced Algebras).
  Applying this tool, an invariant tensor for the M Algebra is constructed,
which serves as the basis upon which a Transgression Gauge Field Theory for the
M Algebra (Chapter 5) is constructed. The relationship between the
four-dimensional dynamics from this theory and the eleven-dimensional torsion
is also considered. Finally, we close with an analysis of the possible
applications of the developed tools, in the context of Cosmology, Supergravity
and String Theory.
