  The problem investigated in this paper is einselection, i. e. the selection
of mutually exclusive quantum states with definite probabilities through
decoherence. Its study is based on a theory of decoherence resulting from the
projection method in the quantum theory of irreversible processes, which is
general enough for giving reliable predictions. This approach leads to a
definition (or redefinition) of the coupling with the environment involving
only fluctuations. The range of application of perturbation calculus is then
wide, resulting in a rather general master equation.
  Two distinct cases of decoherence are then found: (i) A ``degenerate'' case
(already encountered with solvable models) where decoherence amounts
essentially to approximate diagonalization; (ii) A general case where the
einselected states are essentially classical. They are mixed states. Their
density operators are proportional to microlocal projection operators (or
``quasi projectors'') which were previously introduced in the quantum
expression of classical properties.
  It is found at various places that the main limitation in our understanding
of decoherence is the lack of a systematic method for constructing collective
observables.
