  I have chosen, in this presentation of Deformation Quantization, to focus on
3 points: the uniqueness --up to equivalence-- of a universal star product
(universal in the sense of Kontsevich) on the dual of a Lie algebra, the
cohomology classes introduced by Deligne for equivalence classes of
differential star products on a symplectic manifold and the construction of
some convergent star products on Hermitian symmetric spaces. Those subjects
will appear in a promenade through the history of existence and equivalence in
deformation quantization.
