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. Traditional
approaches, for example using Fourier analysis, become awkward to carry
through in situations in which dependence plays an important part,
whereas Stein's method can often still be applied to great effect. In
addition, 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 distribution to be approximated; it
can equally well be normal, or Poisson, or that of the whole path of a
random process, though the techniques have so far been worked out in
much more detail for the classical approximation theorems. This volume
of lecture notes provides a detailed introduction to the theory and
application of Stein's method, in a form suitable for graduate students
who want to acquaint themselves with the method. It includes chapters
treating normal, Poisson and compound Poisson approximation,
approximation by Poisson processes, and approximation by an arbitrary
distribution, written by experts in the different fields. The lectures
take the reader from the very basics of Stein's method to the limits of
current knowledge.