Having introduced the general formalism of difference algebra, and made a more careful study over a complete nonarchimedean field, we specialize to the sort of power series rings over which we studied differential algebra. Most of the rings are ones we have seen before, but we encounter a couple of new variations, notably the Robba ring. This ring consists of power series convergent on some annulus of outer radius 1, but with unspecified inner radius which may vary with the choice of the series. This may seem to be a strange construction at first, but it is rather natural from the point of view of difference algebra: the endomorphisms we will consider (Frobenius lifts) do not preserve the region of convergence of an individual series, but do act on the Robba ring as a whole. This chapter serves mostly to set definitions and notation for what follows. That said, one nontrivial result here is the behavior of the Newton polygon under specialization.