This PhD thesis is a theoretical study of high-current relativistic electron beam transport through solid targets. In the ?rst part, we present an interpretation of a part of experimental results of laser- produced electron beam transport in aluminium foil targets. We have estimated the fast electron beam characteristics and we demonstrated that the collective e?ects dominate the transport in the ?rst tens of μm of propagation. These quantitative estimates were done with the transport models already existing at the beginning of this thesis. These models are no longer su?cient in the case a fast electron beam propagation in insulator targets. Thus, in the second part, we have developed a propagation model of the beam that includes the e?ects of electric ?eld ionization and the collisional ionization by the plasma electrons. We present estimates of the electron energy loss induced by the target ionization, and we discuss its dependence on the beam and target parameters. In the case of a relatively low fast electron density, we demonstrated that the beam creates a plasma where the electons are not in a local thermodynamic equilibrium with ions. We have examined the beam stability and we demonstrated that transverse instabilities can be excited by the relativistic electron beam over the propagation distances of 30 - 300 μm depending on the perturbation wavelength.