Particle Physics theories and experimental discoveries can unravel the misteries of problems of modern Cosmology and Astrophysics: viceversa astronomic observations can constrain theories and models of elementary Particle Physics. An example of this exchange of ideas is offered by the connection between the Dark Matter problem and the Physics theories beyond the Standard Model. The frontiers of experimental Particle Physics will result in the discovery of new particles, hopefully providing a solution to the puzzle of the nature of the dominant fraction of matter content of the Universe, that is to say Dark Matter. A promising solution to the DM problem is offered by the WIMP which appears in certain supersymmetric extensions of the Standard Model, where the lightest particle is a stable, massive and weakly interacting neutralino. Being the neutralinos Majorana particles, they may annihilate into Standard Model particles if the WIMPs in the Milky Way halo accumulate in the core of massive dense objects (like the Sun, the Earth or the Galactic Centre). The detection of neutrinos produced as secondary annihilation product will be the focus of this book.