  The present paper contains a systematic study of the structure of metric Lie
algebras, i.e., finite-dimensional real Lie algebras equipped with a
non-degenerate invariant symmetric bilinear form. We show that any metric Lie
algebra without simple ideals has the structure of a so called balanced
quadratic extension of an auxiliary Lie algebra l by an orthogonal l-module A
in a canonical way. Identifying equivalence classes of quadratic extensions of
l by A with a certain cohomology set H^2_Q(l,A) we obtain a classification
scheme for general metric Lie algebras and a complete classification of metric
Lie algebras of index 3.
