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

PACS numbers: 12.38.Bx