  We study how to generate new Lie algebras $\mathcal{G}(N_0,..., N_p,...,N_n)$
from a given one $\mathcal{G}$. The (order by order) method consists in
expanding its Maurer-Cartan one-forms in powers of a real parameter $\lambda$
which rescales the coordinates of the Lie (super)group $G$, $g^{i_p} \to
\lambda^p g^{i_p}$, in a way subordinated to the splitting of $\mathcal{G}$ as
a sum $V_0 \oplus ... \oplus V_p \oplus ... \oplus V_n$ of vector subspaces. We
also show that, under certain conditions, one of the obtained algebras may
correspond to a generalized \.In\"on\"u-Wigner contraction in the sense of
Weimar-Woods, but not in general. The method is used to derive the M-theory
superalgebra, including its Lorentz part, from $osp(1|32)$. It is also extended
to include gauge free differential (super)algebras and Chern-Simons theories,
and then applied to D=3 CS supergravity.
