  These are the lecture notes of a course taught at the Park City Mathematics
Institute in June 2017. They are intended to review some recent results,
obtained in large part with Thomas Lebl\'e, on the statistical mechanics of
systems of points with logarithmic or Coulomb interactions. After listing some
motivations, we describe the "electric approach" which allows to get
concentration results, Central Limit Theorems for fluctuations, and a Large
Deviations Principle expressed in terms of the microscopic state of the system.
