The evaluation of loop amplitudes via differential equations

The evaluation of loop amplitudes via differential equations and harmonic polylogarithms is discussed at an introductory level. The method is based on evolution equations in the masses or in the external kinematical invariants and on a proper choice of the basis of the trascendental functions. The presentation is pedagogical and goes through specific one-loop and two-loop examples in order to illustrate the general elements and ideas.