Deformational quantization of poisson structures

Questions concerning the notion and properties of Poisson brackets and corresponding formal deformations of function algebras are studied. In particular, a generalization of the Moyal product in the form of the star-product of Drinfelʹd is presented. It is also shown how to produce star products on some Poisson manifolds and Lie Poisson groups using the product of Drinfelʹd.