For 25 years the conception has been well established that the overwhelming majority of chemical elements and their isotopes have been synthesized in stars during the course of stellar evolution, in particular during the advanced stages and in supernova explosions. Until now this general idea has not led to major difficulties or inconsistencies. On the contrary, the theoretical models have been very successful in explaining the observed abundances in meteorites, planets (including the earth), stars (including the sun) and galactic cosmic rays. Our present understanding of nucleosynthesis will be reviewed with special attention given to nucleosynthetic processes in primordial stars and supernovae. We will concentrate primarily on predictions which can be made for relative abundances rather than for absolute abundances, because the latter problem requires evolutionary models of the galaxy which are beyond the scope of this article.