We know that the universe consists of 22\% dark matter. The dark matter particle has to be stable, non-relativistic and only weakly interacting. But we don't know what the dark matter is made of and how it is distributed within our Galaxy. Supersymmetric models predict the existence of the lightest supersymmetric particle (LSP), which is stable if R-parity is conserved. In supersymmetric models inspired by supergravity, the commonly accepted LSP candidate is the lightest neutralino which is a neutral and weakly interacting massive particle. It is a viable candidate for dark matter since the derived relic abundance is naturally within the observed range. In general, the cosmic antiparticles are expected as secondary products of interactions ...