  Recently proposed supergravity theories in odd dimensions whose fields are
connection one-forms for the minimal supersymmetric extensions of anti-de
Sitter gravity are discussed. Two essential ingredients are required for this
construction: (1) The superalgebras, which extend the adS algebra for different
dimensions, and (2) the lagrangians, which are Chern-Simons $(2n-1)$-forms. The
first item completes the analysis of van Holten and Van Proeyen, which was
valid for N=1 only. The second ensures that the actions are invariant by
construction under the gauge supergroup and, in particular, under local
supersymmetry. Thus, unlike standard supergravity, the local supersymmetry
algebra closes off-shell and without requiring auxiliary fields. \\
  The superalgebras are constructed for all dimensions and they fall into three
families: $osp(m|N)$ for $D=2,3,4$, mod 8, $osp(N|m)$ for $D=6,7,8$, mod 8, and
$su(m-2,2|N)$ for D=5 mod 4, with $m=2^{[D/2]}$. The lagrangian is constructed
for $D=5, 7$ and 11. In all cases the field content includes the vielbein
($e_{\mu}^{a}$), the spin connection ($\omega_{\mu}^{ab}$), $N$ gravitini
($\psi_{\mu}^{i}$), and some extra bosonic "matter" fields which vary from one
dimension to another.
