Electron beam energies in Transmission Electron Microscopes (TEMs) reach the relativistic realm constituting Quantum Electrodynamics (QED) the appropriate framework for the study of electron matter interaction in TEMs. We focus on the inelastic scattering of relativistic electrons from a generic oriented target. The inelastic differential cross section factorizes to the fast electron part which is calculated analytically, and the dynamic form factor of the target, which encodes the response of the medium to the interaction with the beam. The properties of the dynamic form factor of oriented targets are analyzed. We then derive the scattering cross section of electrons by magnetic targets where spin-flip transitions are induced. We comment on the kinematic regimes where the coefficient of the transverse magnetic interaction is amplified compared to the coulomb matrix element.