In these notes we review the foundations of Banach--Poisson geometry
and explain how in this framework one obtains a unified approach
to the Hamiltonian and the quantum mechanical description of the
physical systems. Our considerations will be based on the notion of
Banach Lie--Poisson space and the notion of the coherent state map,
which appear to be the crucial instrument for the clarifying what is
the quantization of the classical physical (Hamiltonian) system.
