Abstract: A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. The method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the approximating distribution; it can equally well be normal, or Poisson, or that of the whole path of a random process. The method involves solving a functional equation such as a differential equation, difference equation or integral equation. These lectures will cover mainly normal approximation and Poisson approximation.