  An elementary presentation of the methods for the canonical quantization of
constraint systems with Fermi variables is given. The emphasis is on the
subtleties of the construction of an appropriate classical bracket that could
be consistently replaced by commutators or anti--commutators of operators, as
required by canonical quantization procedure for bosonic and fermionic degrees
of freedom respectively. I present a consequent canonical quantization of the
Dirac field, in which the role of Poincar\'e invariance is made marginal. This
simple example provides an introduction to the Poincar\'e--free quantization of
spinor electrodynamics in the second part of the paper.
