  This is an expanded version of a three-hour minicourse given at the
winterschool Winterbraids IV held in Dijon in February 2014. The aim of these
lectures was to present some aspects of the dimer model to a geometrically
minded audience. We spoke neither of braids nor of knots, but tried to show how
several geometrical tools that we know and love (e.g. (co)homology, spin
structures, real algebraic curves) can be applied to very natural problems in
combinatorics and statistical physics. These lecture notes do not contain any
new results, but give a (relatively original) account of the works of
Kasteleyn, Cimasoni-Reshetikhin and Kenyon-Okounkov-Sheffield.
