  In this work we give a deformation theoretical approach to the problem of
quantization. First the notion of a deformation of a noncommutative ringed
space over a commutative locally ringed space is introduced within a language
coming from Algebraic Geometry and Complex Analysis. Then we define what a
Dirac quantization of a commutative ringed space with a Poisson structure, the
space of classical observables, is. Afterwards the normal order quantization of
the Poisson space of classical polynomial observables on a cotangent bundle is
constructed. By using a complete symbol calculus on manifolds we succeed in
extending the normal order quantization of polynomial observables to a
quantization of a Poisson space of symbols on a cotangent bundle. Furthermore
we consider functorial properties of these quantizations. Altogether it is
shown that a deformation theoretical approach to quantization is possible not
only in a formal sense but also such that the deformation parameter $\hbar$ can
attain any real value.
