Third-order nonlinear spectroscopies are the most widely used class of nonlinear methods, including the common pump-probe experiment. The approach here is meant to be practical, with the emphasis on t...Third-order nonlinear spectroscopies are the most widely used class of nonlinear methods, including the common pump-probe experiment. The approach here is meant to be practical, with the emphasis on trying to connect the particular signals with their microscopic origin. This approach can be used for describing any experiment in terms of the wave-vector, frequency and time-ordering of the input fields, and the frequency and wavevector of the signal.