2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58868I 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.Text of my talk at the Moshe Flato conference in Dijon in September 1999Differential Geometry53D55text