  These notes originated in a series of lectures I gave in Marseille in May,
2013. I was invited to give an introduction to the isomorphism theorems,
originating with Dynkin, which connect Markov local times and Gaussian
processes. This is an area I had worked on some time ago, and even written a
book about, but had then moved on to other things. However, isomorphism
theorems have become of interest once again, both because of new applications
to the study of cover times of graphs and Gaussian fields, and because of new
isomorphism theorems for non-symmetric Markov processes and their connection
with loop soups and Poisson processes. Thus I felt the time was ripe for a new
introduction to this topic.
  In these notes I have tried to preserve the informal atmosphere of the
lectures, and often simply refer the reader to my book and other sources for
details.
