  The abstract mathematical structure behind the positive energy quantization
of linear classical systems is described. It is separated into 3 stages: the
description of a classical system, the algebraic quantization and the Hilbert
space quantization. 4 kinds of systems are distinguished: neutral bosonic,
neutral bosonic, charged bosonic and charged fermionic. The formalism that is
described follows closely the usual constructions employed in quantum physics
to introduce non-interacting quantum fields.
