  This is a short presentation of some classical results on finite dimensional
complex Lie algebras (classification of nilpotent Lie algebras, deformations
and perturbations, contractions and rigidity). We present some applications to
Differential Geometry considering some left invariant structures on Lie groups
: contact and symplectic structures, Generalized complex structures on real Lie
Group. We present also the notion of riemannian and pseudo-riemannian
G-symmetric spaces.
