  In the paper is presented an invariant quantization procedure of classical
mechanics on the phase space over flat configuration space. Then, the passage
to an operator representation of quantum mechanics in a Hilbert space over
configuration space is derived. An explicit form of position and momentum
operators as well as their appropriate ordering in arbitrary curvilinear
coordinates is demonstrated. Finally, the extension of presented formalism onto
non-flat case and related ambiguities of the process of quantization are
discussed.
