This thesis presents the study of the slowing down process of fast heavy ions inside matter. In the framework of this research, the influence of the target density on the stopping process is investigated. Experiments on the interaction of 48Ca6+ - 48Ca10+ and 26Mg5+ ion beams with initial energies of 11.4 MeV/u and 5.9 MeV/u with solid and gaseous targets have been carried out. A novel diagnostic method, X-ray spectroscopy of K-shell projectile radiation, is used to determine the ion charge state in relation to its velocity during the penetration of fast heavy ions inside the stopping material. A spatially resolved analysis of the projectile and target radiation in solids is achieved for the first time. The application of low-density silica aerogels as stopping media provided a stretching of the ion stopping length by 20 - 100 times in comparison with solid quartz. The Doppler Effect observed on the projectile K-shell spectra is used to calculate the ion velocity in dependence on the ion penetration depth in the target material. A comparative analysis of K_alpha spectra of fast heavy ions is performed in solid (silica aerogels) and gaseous targets (Ar and Ne gases) at the same ion energy. It is shown that the dominant role of collisions in dense matter leads to an increase of the effective ionization cross section at high ion velocity and suppression of the electron capture to the projectile ion excited states at low ion velocity. As a result, an increase of the ion charge state in dense matter is observed. The experimentally detected effects are interpreted with numerical calculations of the projectile population kinetics, which are in good agreement with measurements.