In this book the nuclear many-body problem is treated either with a pure quantum approach with various approximations or by using some phenomenological ideas (like the liquid-drop and related models). It is also shown how to work with new techniques such as semiclassical methods in nucleus-nucleus scattering and the microscopic semiclassical approach to nuclear many-body problem, and a discussion closely related to experimental problems is presented. A complete analysis of the phase space approach is also included. Several applications of these new techniques to the description of collective motions and of heavy ion collisions in relation also to experimental problems is shown.