We present experimental and numerical results on intense-laser-pulse-produced fast electron beams transport through aluminum samples, either solid or compressed and heated by laser-induced planar shock propagation. Thanks to absolute K yield measurements and its very good agreement with results from numerical simulations, we quantify the collisional and resistive fast electron stopping powers: for electron current densities of % 8 Â 10 10 A=cm 2 they reach 1:5 keV= m and 0:8 keV= m, respectively. For higher current densities up to 10 12 A=cm 2 , numerical simulations show resistive and collisional energy losses at comparable levels. Analytical estimations predict the resistive stopping power will be kept on the level of 1 keV= m for electron current densities of 10 14 A=cm 2 , representative of the full-scale conditions in the fast ignition of inertially confined fusion targets. In the fast ignition (FI) scheme of inertial confinement fusion, a relativistic electron beam (REB) heats the compressed core and ignites the fusion reactions in a capsule of deuterium and tritium [1]. This REB is generated at the critical density surface, or at the cone tip of a cone-embedded imploded capsule [2] by a high-intensity (% 10 20 W=cm 2 ) and high-energy ($100 kJ) laser. The REB source has a total kinetic energy & 40% of the laser energy [3][4][5] and a mean kinetic energy of 1-2 MeV (to provide an efficient coupling to the dense core). The REB transports energy from the generation region (with density and temperature in the level of a few g=cm 3 and a few eV, respectively) to the high-density ($ 400 g=cm 3 ) and hightemperature ($ 300 eV) core, where it must deliver a minimum of 20 kJ to heat the fuel to thermonuclear temperatures ($ 5-10 keV) [6]. The energy transport efficiency can be limited by such physical processes as collisional or collective energy loss [7], divergence [8,9], filamentation [10][11][12], etc. The energy losses over the highly inhomogeneous electron transport zone should be accurately predicted for a successful full-scale FI design. In particular, the REB stopping power should be limited to a few keV= m over the $100 m standing-off distance between the REB source and the imploded core.The work presented here aims at characterizing the REB stopping power in dense media in underscaled experimental conditions. The measurements are used to benchmark a REB transport code. The tested transport media, ranging from solid to warm dense matter, are much denser than the injected REB, being reasonable to assume an efficient neutralization of the injected current (j h ) by a counterstreaming current (j e ) of background thermal electrons (j h % Àj e ). Under these conditions, the numerical description of the REB transport often uses the so-called hybrid approach, where the incident and weakly collisional electrons are modeled kinetically and the highly collisional return current is described as an inertialess fluid [10,13,14].Most of the REB transport experiments carried out up to now have used solid targets [8,15...