I'm a condensed matter physicist who tries to understand the details of deformation quantization.
In my self-made training, I've found two huge pieces of work, namely
Fedosov, B. V. (1994). "A simple geometrical construction of deformation quantization". Journal of Differential Geometry, 40 : 213–238.
Kontsevich, M. (2003). "Deformation Quantization of Poisson Manifolds". Letters in Mathematical Physics, 66 : 157-216.
[remarks : Fedosov's work seems to be also available with details in a book Deformation quantization and index theory. Are the two references overlapping ? -- I've found several documents from Kontsevich having similar titles, from 1997 to 2003, but I've no access to the reference of 2003, is the arXiv version the same as the final one ?]
My problem is that these works are really deep, long and difficult to me, so before continuing reading them, I'd like to understand whether these two works are equivalent or not, if they overlap somehow, and which kind of problem these works solved. If the answers could be without too much details for a physicist I'd really appreciate continuing learning this interesting topic.