  In this contribution, we present the geometric approach to supergravity. In
the first part, we discuss in some detail the peculiarities of the approach and
apply the formalism to the case of pure supergravity in four space-time
dimensions. In the second part, we extend the discussion to theories in higher
dimensions, which include antisymmetric tensors of degree higher than one,
focussing on the case of eleven dimensional space-time. Here, we report the
formulation first introduced in 1981 by R. D'Auria and P. Fr\`e, corresponding
to a generalization of a Chevalley-Eilenberg Lie algebra, together with some
more recent results, pointing out the relation of the formalism with the
mathematical framework of $L_\infty$ algebras.
