  These lecture notes present an introduction to classical Affine Gaudin
models, which provide a general framework for the systematic construction and
study of a large class of integrable two-dimensional field theories. A key role
is played by Kac-Moody currents, which are fields satisfying a particular
Poisson bracket. After reviewing this notion, we discuss in detail the
construction of Affine Gaudin models in the language of Hamiltonian field
theories. Special emphasis is placed on their symmetries and conserved
quantities, including the construction of infinite families of local and
non-local Poisson-commuting charges in terms of Kac-Moody currents. Moreover,
we study explicit examples of affine Gaudin models, making the link with the
realm of integrable sigma-models. Finally, we mention briefly various
perspectives concerning these theories, including the question of their
quantisation.
  Minimal prerequisites on classical Hamiltonian field theories and
integrability are required to follow the presentation and a brief reminder of
these notions is given at the beginning of the notes. Moreover, various
exercises are included throughout the document. These notes were prepared for
the Young Researchers Integrability School and Workshop held in Durham from 17
to 21 July 2023.
