  This is a set of notes recalling some of the most important results on the XY
model from the ground up. They are meant for a junior researcher wanting to get
accustomed to the Kosterlitz-Thouless phase transition in the context of the 2D
classical XY model. The connection to the 2D Coulomb gas is presented in
detail, as well as the renormalization group flow obtained from this dual
representation. A numerical Monte-Carlo approach to the classical XY model is
presented. Finally, two physical setting that realize the celebrated
Kosterlitz-Thouless phase transition are presented: superfluid and liquid
crystal thin films.
