While the primordial (or Big Bang) nucleosynthesis delivers important clues about the conditions in the high red-shift universe (termed far-field cosmology), the nucleosynthesis of the heavy elements beyond iron by the r-process or the s-process deliver information about the early phase and history of the Galaxy (termed near-field cosmology). In particular, the r-process nucleosynthesis is unique, because it is a primary process that helps to associate individual stars with the composition of the protocloud. The present contribution is intended to give a brief overview about these nucleosynthesis processes and describe their link to the early universe, stellar evolution and to the chemical evolution of the Galaxy. The focus of this present contribution is on illumination the role of nucleosynthesis in the Universe.