This book is the added and revised publication of the previous author's book "Thermonuclear processes of the Universe", New-York, NOVA Sci. Publ., 2012, 194p. The first chapter contains the review of thermonuclear processes in the Sun and stars. The second is devoted to the description of the using model and basic calculation methods of some characteristics for bound states and continuum of nuclear particles. In the rest 13th chapters, the radiative capture processes for the p2H, p3H, p6Li, p7Li, p9Be, p10B, p11B, p12C, p13C, p14C, p15N, and also 2H4He, 3H4He, 3H¿4He, 4He12C systems were considered at astrophysical energies. It was shown that using approach allows one to describe available experimental data comparatively well in this energy range. Besides, it was shown that in some cases, for certain nuclear systems, it was possible to predict the behavior of the S-factor at energies lower than 100-200 keV, because these calculations were published in 1995, and new experimental data were appeared only in 1997-2002 years.