This monograph focuses on the influence of a strong magnetic field on the interactions between charged particles in a many-body system. It is the only book available on the topic. The book focuses on the influence of a strong magnetic field on the interactions between charged particles in a many-body system. Two complementary approaches, the binary collision model and the dielectric theory are investigated in both analytical and numerical frameworks. In the binary collision model, the Coulomb interaction between the test and the target particles is screened because of the polarization of the target.