  A `discrete differential manifold' we call a countable set together with an
algebraic differential calculus on it. This structure has already been explored
in previous work and provides us with a convenient framework for the
formulation of dynamical models on networks and physical theories with discrete
space and time. We present several examples and introduce a notion of
differentiability of maps between discrete differential manifolds. Particular
attention is given to differentiable curves in such spaces. Every discrete
differentiable manifold carries a topology and we show that differentiability
of a map implies continuity.
