This is an introductory text, in two parts, on scaling limits and modelling in equations of mathematical physics. The first part is concerned with basic concepts of the kinetic theory of gases which is not only important in its own right but also as a prototype of a mathematical construct central to the theory of non-equilibrium phenomena in large systems. It also features a very readable historic survey of the field. The second part dwells on the role of integrable systems for modelling weakly nonlinear equations which contain the effects of both dispersion and nonlinearity. Starting with a...