Presented book is the first part of the previous book “Primordial Nucleosynthesis in the Universe”, 2014. 668p. (Lambert Academic Publ.) essentially revised and enlarged. Chapter 1 is describing the general methods for the calculation of the basic characteristics of the bound states and continuum, as well as the phase shift analysis of elastic nuclear scattering. Chapter 2 illustrates the methods and computing programs for reconstructing of elastic scattering phase shifts for the 4Не4Не, n3He, р6Li, p12C, n12C, р13С, р14С, n16O, p16O, and 4Не12C nuclear systems at low and astrophysical energies. These results may be applied for the construction of the corresponding interaction potentials for the purposes of nuclear astrophysical problems. Chapter 3 includes the results on the three-body calculations of some light nuclear systems based on the pair potentials obtained in frame of phase shift analyses. The book will be useful for undergraduates, PhD doctorates and some scientists in the field of nuclear physics.