  The Gaussian Free Field (GFF) in the continuum appears to be the natural
generalisation of Brownian motion, when one replaces time by a multidimensional
continuous parameter. The goal of these lecture notes is to describe some
aspects of the continuum GFF and of its discrete counterpart defined on
lattices, with the aim of providing a gentle self-contained introduction to
some recent developments on this topic, such as the relation between the
continuum GFF, Brownian loop-soups and the Conformal Loop Ensembles CLE(4).
  This is an updated and expanded version of the notes written by the first
author for graduate courses at ETH Z\"urich. The exercises that are
interspersed in the first half of these notes mostly originate from the
exercise sheets prepared by the second author for this course in 2018.
