  The quest for unification of particles and fields and for reconciliation of
Quantum Mechanics and General Relativity has led us to gauge theories, string
theories, supersymmetry and higher-extended objects: membranes... Our spacetime
is quantum mechanical but it admits semiclassical descriptions of various
``complementary'' kinds that could be valid approximations in various
circumstances. One of them might be supergravity in 11 dimensions the largest
known interacting theory of a finite number of fields with gauged Poincar\' e
supersymmetry. Its solitons and their dual membranes would be states in its
quantum version called M-theory. We shall review the construction of its
classical action by deformation of a globally supersymmetric free theory and
its on-shell superspace formulation. Then we shall focus on the bosonic matter
equations of the dimensional reductions on tori of dimensions 1 to 8 to exhibit
their common self-duality nature. In the concluding section we shall discuss
possible remnants at the quantum level and beyond the massless sector of
generalised discrete U-dualities. We shall also comment on the variable
dimension of spacetime descriptions and on the possibility of extending the
self dual description to spacetime itself and its metric.
