Abstract. The study of the energy production in stars and related nucleosyntesis processes requires increasingly precise knowledge of the nuclear reaction cross section and reaction rates at interaction energy. In order to overcome the experimental difficulties, arising from small cross-sections involved in charge particle induced reactions at astrophysical energies, and from the presence of electron screening, it was necessary to introduce indirect methods. Trough these methods it is possible to measure cross sections at very small energies and retrieve information on electron screening effect when ultra-low energy direct measurements are available. The Trojan Horse Method (THM) represents the indirect technique to determine the bare nucleus astrophysical S-factor for reactions between charged particles at astrophysical energies. The basic theory of the THM is discussed in the case of non-resonant.