  Following our approach to metric Lie algebras developed in math.DG/0312243 we
propose a way of understanding pseudo-Riemannian symmetric spaces which are not
semi-simple. We introduce cohomology sets (called quadratic cohomology)
associated with orthogonal modules of Lie algebras with involution. Then we
construct a functorial assignment which sends a pseudo-Riemannian symmetric
space M to a triple consisting of
  (i) a Lie algebra with involution (of dimension much smaller than the
dimension of the transvection group of M),
  (ii) a semi-simple orthogonal module of the Lie algebra with involution, and
  (iii) a quadratic cohomology class of this module.
  That leads to a classification scheme of indecomposable non-simple
pseudo-Riemannian symmetric spaces. In addition, we obtain a full
classification of symmetric spaces of index 2 (thereby completing and
correcting in part earlier classification results due to Cahen/Parker and
Neukirchner math.DG/0301326).
