Nonlinear evolution equations in QCD

The following lectures are an introduction to the phenomena of partonic saturation and nonlinear evolution equations in Quantum Chromodynamics. After a short introduction to the linear evolution, the problems of unitarity bound and parton saturation are discussed. The nonlinear Balitsky-Kovchegov evolution equation in the high energy limit is introduced, and the progress towards the understanding of the properties of its solution is reviewed. We discuss the concepts of the saturation scale, geometrical scaling and the lack of the infrared diffusion. Finally, we give a brief summary of current theoretical developments which extend beyond the Balitsky-Kovchegov equation.