Peter Gustav Lejeune Dirichlet
An introduction to Dirichlet spaces: Lecture notes
The outline of those (unpolished) lecture notes is the following:
Chapter 1: Semigroups
Chapter 2: Markovian semigroups and Dirichlet forms
Chapter 3: Dirichlet spaces with Gaussian or sub-Gaussian heat kernel estimates
Chapter 4: Strictly local Dirichlet spaces
Research and Lecture notes 