In Chap. 8 we have presented the scattering theory of a particle interacting with another independent particle by some potential interaction \(V(\textbf{r})\) and defined the relevant quantities such as the scattering amplitude and the differential cross section. In this chapter we will provide the formal scattering theory for many-particle systems, which will end up in the definition of the S-matrix, the general T-matrix and Born-series.