  As part of stratification of Cohen-Macaulay rings, we introduce and develop
the theory of Goto rings, generalizing the notion of almost Gorenstein rings
originally defined by V. Barucci and R. Fr\"oberg in 1997. What has dominated
the series of researches on almost Gorenstein rings is the fact that the
reduction numbers of extended canonical ideals are at most $2$; we define Goto
rings as Cohen-Macaulay rings admitting such extended canonical ideals. We
provide a characterization of Goto rings in terms of the structure of Sally
modules and determine the Hilbert functions of them. Various examples of Goto
rings that come from numerical semigroups, idealizations, fiber products, and
equimultiple Ulrich ideals are explored as well.
