  A general framework of constructions of endoscopy correspondences via
automorphic integral transforms for classical groups is formulated in terms of
the Arthur classification of the discrete spectrum of square-integrable
automorphic forms. This suggests a principle, which is called the
$(\tau,b)$-theory of automorphic forms of classical groups, to reorganize and
extend the series of work of Piatetski-Shapiro, Rallis, Kudla and others on
standard $L$-functions of classical groups and theta correspondence.
