  I prove that every finite-dimensional Poisson manifold X admits a canonical
deformation quantization. Informally, it means that the set of equivalence
classes of associative algebras close to the algebra of functions on X is in
one-to-one correspondence with the set of equivalence classes of Poisson
structures on X modulo diffeomorphisms. In fact, a more general statement is
proven ("Formality conjecture"), relating the Lie superalgebra of polyvector
fields on X and the Hochschild complex of the algebra of functions on X.
Coefficients in explicit formulas for the deformed product can be interpreted
as correlators in a topological open string theory, although I do not use
explicitly the language of functional integrals. One of corollaries is a
justification of the orbit method in the representation theory.
