In the first part of this PhD thesis, 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 effects dominate the transport in the first tens of microns of propagation. These quantitative estimates were done with transport models already existing at the beginning of this thesis. These models are no longer sufficient 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 effects of electric field ionization and the collisional ionization by the plasma electrons. We present estimates of the electron energy loss induced by the target ionization. For a low beam 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