  This script is based on the notes the author prepared to give a set of six
lectures at the Les Houches School "Integrability in Atomic and Condensed
Matter Physics" in the summer of 2018. The school had its focus on the
application of integrability based methods to problems in non-equilibrium
statistical mechanics. The lectures were meant to complement this subject with
background material on the equilibrium statistical mechanics of quantum spin
chains from a vertex model perspective. The author was asked to provide a
minimal introduction to quantum spin systems including notions like the reduced
density matrix and correlation functions of local observables. He was further
asked to explain the graphical language of vertex models and to introduce the
concepts of the Trotter decomposition and the quantum transfer matrix. This was
basically the contents of the first four lectures presented at the school. In
the remaining two lectures these notions were filled with life by deriving an
integral representation of the free energy per lattice site for the
Heisenberg-Ising chain (alias XXZ model) using techniques based on non-linear
integral equations.
