This monograph focusses 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. In the continuum dielectric theory one considers the interactions between the test particle and its polarization cloud. In the presence of a strong magnetic field, there exists no suitable parameter of smallness. Linearized and perturbative treatments are not more valid and must be replaced by numerical grid or particle methods. Applications include the electron cooling of ion beams in storage rings and the final deceleration of antiprotons and heavy ion beams in traps.