Integrability in gauge theories

In these lectures, I shall explain the general phenomenon of integrability in four-dimensional gauge theories choosing as a prime example calculation of the anomalous dimensions of various Wilson operators in Yang-Mills theory and its supersymmetric extensions. I will demonstrate that to lowest order of perturbative expansion the mixing matrix for such operators inherits a conformal symmetry of the classical Lagrangian and, most importantly, it can be mapped into a Hamiltonian of the celebrated Heisenberg spin chain and its generalizations. Finally, a short overview of the Bethe Ansatz approach to calculation of anomalous dimensions will be given.