  A unified scheme for treating generalized superselection sectors is proposed
on the basis of the notion of selection criteria to characterize states of
relevance to each specific domain in quantum physics, ranging from the
relativistic quantum fields in the vacuum situations with unbroken and
spontaneously broken internal symmetries, through equilibrium and
non-equilibrium states to the some basic aspects in measurement processes. This
is achieved by the help of \textit{c} $\to$ \textit{q} and \textit{q} $\to$
\textit{c} channels, the former of which determines the states to be selected
and to be parametrized by the order parameters defined as the spectrum of the
centre constituting the superselection sectors, and the latter of which
provides, as classifying maps, the physical interpretations of selected states
in terms of order parameters. This formulation extends the traditional range of
applicability of the Doplicher-Roberts construction method for recovering the
field algebra and the gauge group (of the first kind) from the data of group
invariant observables to the situations with spontaneous symmetry breakdown, as
will be reported in a succeeding paper.
