Any author who is going to write a mathematical text on a topic in statistical physics, and in particular if he or she wants to treat the problem of deriving the macroscopic behavior of a large system from its microscopic
structure, will necessarily have to expose the concept of the two different scales (macro and micro) in space and in time, and his central problem will be to establish theorems transforming that concept into precise mathematical statements. In the concrete case of the present book, it is clear from the title that we will be faced with this type of problem, even more: that the objects of study are systems evolving in time and not equilibrium properties of large systems.