In this seminar, we discuss sheaves of (h-adic) vertex algebras on symplectic manifolds, which give quantization of vertex Poisson algebras of their Jet bundles. On each formal coordinate, these sheaves are isomorphic to the vertex algebra of a formal beta-gamma system and we can determine the Lie algebra of derivations. Using Harish-Chandra extensions, we consider the classification of such sheaves. Such sheaves include localization of
affine W-algebras which were constructed by Arakawa, Malikov and the speaker. Moreover, they include quantization of Jet bundles of hypertoric varieties and Nakajima quiver varieties. We also discuss construction of such quantization by semi-infinite reduction.