Nuclear astrophysics is a relatively young science; it is about half a century old. It is a multidisciplinary subject, since it combines nuclear physics with astrophysics and observations in astronomy. It also addresses fundamental issues in astrobiology through the formation of elements, in particular those required for a carbon-based life. In this paper, a rapid overview of nucleosynthesis is given, mainly from the point of view of nuclear physics. A short historical introduction is followed by the definition of the relevant nuclear parameters, such as nuclear reaction cross sections, astrophysical S-factors, the energy range defined by the Gamow peak and reaction rates. The different astrophysical scenarios that are the sites of nucleosynthesis, and different processes, cycles and chains that are responsible for the building of complex nuclei from the elementary hydrogen nuclei are then briefly described.