Integrability and symmetries of difference equations: the Adler-Bobenko-Suris case

We consider the partial difference equations of the Adler-Bobenko-Suris classification,which are characterizedas multidimensionally consistent. The latter property leads naturallyto the construction of auto-B ?acklund transformations and Lax pairs for all the equations in this class. Their symmetry analysis is presented and infinite hierarchies of generalized symmetries are explicitly constructe