Books on Differential Operators include: Coutinho "A Primer of Algebraic D-modules" which discusses lots about the Weyl algebra and its ring theory; Hotta, Takeuchi, Tanisaki "D-modules, Perverse Sheaves, and Representation Theory" which builds up the machinery necessary to prove the Beilinson-Bernstein theorem and prove the Kazhdan-Lusztig Conjecture.
The statement and proof of a Beilinson-Bernstein theorem for general weights can be found in the paper of Backelin-Kremnizer.
There are two good surveys about symplectic singularities: one by Kaledin, the other by Fu.
These lectures refer to articles of Namikawa - here and here - and Kaledin (the one above), as well as the book on "Deformation Theory" by Hartshorne.
This lecture uses articles of Bezrukavnikov-Kaledin - here - and Kashiwara-Rouquier here.
This lecture uses the above article of Kashiwara-Rouquier, plus the following: Nakajima, Etingof-Ginzburg , Gordon-Stafford, Gan-Ginzburg.
This lecture refers to the following: Bellamy-Kuwabara and Braden-Licata-Proudfoot-Webster.
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