A general framework for 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, which is called the Principle of Endoscopy Correspondences,
extending the well-known Howe Principle of Theta Correspondences.
This suggests another principle, called the (τ, 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.