  In these introductory lectures we discuss the topic of Yangian symmetry from
various perspectives. Forming the classical counterpart of the Yangian and an
extension of ordinary Noether symmetries, first the concept of nonlocal charges
in classical, two-dimensional field theory is reviewed. We then define the
Yangian algebra following Drinfeld's original motivation to construct solutions
to the quantum Yang-Baxter equation. Different realizations of the Yangian and
its mathematical role as a Hopf algebra and quantum group are discussed. We
demonstrate how the Yangian algebra is implemented in quantum, two-dimensional
field theories and how its generators are renormalized. Implications of Yangian
symmetry on the two-dimensional scattering matrix are investigated. We
furthermore consider the important case of discrete Yangian symmetry realized
on integrable spin chains. Finally we give a brief introduction to Yangian
symmetry in planar, four-dimensional super Yang-Mills theory and indicate its
impact on the dilatation operator and tree-level scattering amplitudes. These
lectures are illustrated by several examples, in particular the two-dimensional
chiral Gross-Neveu model, the Heisenberg spin chain and N=4 superconformal
Yang-Mills theory in four dimensions. This review arose from lectures given at
the Young Researchers Integrability School at Durham University (UK).
