**Symmetries of integrable difference equations**

**Abstract:**

This talk describes our approach to symmetries of integrable difference equations in the famous
Adler-Bobenko-Suris (ABS) classification. By using the direct method, we have been able to obtain point symmetries and
higher symmetries for each of the ABS equations. In particular, we have found mastersymmetries for each equation – these
produce an infinite hierarchy of local symmetries. We also demonstrate a connection between the symmetries
of quad-graph equations and those of the corresponding Toda type difference
equations.