  These notes were used in a short graduate course on branching processes the
author gave in Beijing Normal University. The following main topics are
covered: scaling limits of Galton--Watson processes, continuous-state branching
processes, extinction probabilities, conditional limit theorems, decompositions
of sample paths, martingale problems, stochastic equations, Lamperti's
transformations, independent and dependent immigration processes. Some of the
results are simplified versions of those in the author's book "Measure-valued
branching Markov processes" (Springer, 2011). We hope these simplified results
will set out the main ideas in an easy way and lead the reader to a quick
access of the subject.
