  After a self-contained introduction to Lie algebra cohomology, we present
some recent applications in mathematics and in physics. Contents:
  1. Preliminaries: L_X, i_X, d
  2. Elementary differential geometry on Lie groups
  3. Lie algebra cohomology: a brief introduction
  4. Symmetric polynomials and higher order cocycles
  5. Higher order simple and SH Lie algebras
  6. Higher order generalized Poisson structures
  7. Relative cohomology, coset spaces and effective WZW actions
