  We introduce a universally applicable method, based on the bond-algebraic
theory of dualities, to search for generalized order parameters in disparate
systems including non-Landau systems with topological order. A key notion that
we advance is that of {\em holographic symmetry}. It reflects situations
wherein global symmetries become, under a duality mapping, symmetries that act
solely on the system's boundary. Holographic symmetries are naturally related
to edge modes and localization. The utility of our approach is illustrated by
systematically deriving generalized order parameters for pure and
matter-coupled Abelian gauge theories, and for some models of topological
matter.
