The theory of (ordinary and partial) differential equations is well-established and to some extent standardised. By contrast, the theory of difference equations, while more fundamental, has until recently been in its infancy, in spite of a major effort at the beginning of the 20th Century by N"orlund and the school of G.D. Birkhoff to establish the linear theory. Discrete systems can appear in two main guises: in the first case the independent variable is discrete, taking values on a lattice (e.g. finite-difference equations, such as recurrence relations and dynamical mappings), in the...