This paper proves that any finite-dimensional Poisson manifold can be canonically quantized through deformation quantization. The key result is the Formality conjecture, which states that the Hochschild complex of the algebra of polynomials is quasi-isomorphic to the graded Lie algebra of polyvector fields. This conjecture is proven using ideas from string theory and involves constructing a quasi-isomorphism between these structures. The paper introduces the concept of $ L_{\infty} $-morphisms and quasi-isomorphisms, which are essential for comparing deformation theories of differential graded Lie algebras. The main result is the existence of a quasi-isomorphism between the Hochschild complex of the polynomial algebra and the graded Lie algebra of polyvector fields, which implies the Formality conjecture for affine spaces. The proof uses the Stokes formula and vanishing theorems for integrals over configuration spaces. The results are extended to general manifolds by considering formal geometry and superconnections. The paper also discusses the cup-product on the tangent bundle to the super moduli space and its compatibility with the quantization. The Formality conjecture has implications for the orbit method in representation theory and the Duflo-Kirillov formulas for Lie algebras. The paper also touches on applications to Mirror Symmetry and quantum field theory. The main theorem shows that the set of gauge equivalence classes of star-products on a smooth manifold is naturally identified with the set of equivalence classes of Poisson structures. The paper provides an explicit universal formula for the star-product in terms of bidifferential operators and graphs, and discusses the deformation theory of associative algebras using differential graded Lie algebras. The paper concludes with a sketch of the proof of the main theorem, showing that any $ L_{\infty} $-algebra is quasi-isomorphic to a minimal one, and that quasi-isomorphisms induce isomorphisms between deformation functors.This paper proves that any finite-dimensional Poisson manifold can be canonically quantized through deformation quantization. The key result is the Formality conjecture, which states that the Hochschild complex of the algebra of polynomials is quasi-isomorphic to the graded Lie algebra of polyvector fields. This conjecture is proven using ideas from string theory and involves constructing a quasi-isomorphism between these structures. The paper introduces the concept of $ L_{\infty} $-morphisms and quasi-isomorphisms, which are essential for comparing deformation theories of differential graded Lie algebras. The main result is the existence of a quasi-isomorphism between the Hochschild complex of the polynomial algebra and the graded Lie algebra of polyvector fields, which implies the Formality conjecture for affine spaces. The proof uses the Stokes formula and vanishing theorems for integrals over configuration spaces. The results are extended to general manifolds by considering formal geometry and superconnections. The paper also discusses the cup-product on the tangent bundle to the super moduli space and its compatibility with the quantization. The Formality conjecture has implications for the orbit method in representation theory and the Duflo-Kirillov formulas for Lie algebras. The paper also touches on applications to Mirror Symmetry and quantum field theory. The main theorem shows that the set of gauge equivalence classes of star-products on a smooth manifold is naturally identified with the set of equivalence classes of Poisson structures. The paper provides an explicit universal formula for the star-product in terms of bidifferential operators and graphs, and discusses the deformation theory of associative algebras using differential graded Lie algebras. The paper concludes with a sketch of the proof of the main theorem, showing that any $ L_{\infty} $-algebra is quasi-isomorphic to a minimal one, and that quasi-isomorphisms induce isomorphisms between deformation functors.