Nucleosynthesis is the science related to all astrophysical processes which are responsible for the abundances of the elements and their isotopes in the universe. The astrophysical sites are the big bang and stellar objects. The working of nucleosynthesis processes is presented in a survey of events which act as abundance sources. For intermediate-mass and heavy elements, these are stellar evolution, type la and core collapse supernovae as well as hypernovae. We discuss successes and failures of existing processes and possible solutions via new (hitherto unknown) processes. Finally an analysis of their role is given in the puzzle to explain the evolution of the elemental and isotopic compositions found in galaxies, and especially the mixture found in the solar system. Different timescales due to the progenitor mass dependence of the endpoints of stellar evolution (type II supemova. explosions - SNe II vs. planetary nebulae) or single vs. binary stellar systems (the latter being responsible for novae, type la supernovae - SNe la, or X-ray bursts) are the keys to understand galactic evolution. At very early times, the role of explosion energies of events, polluting pristine matter with a composition originating only from the big bang, might also play a role. We also speculate on the role of very massive stars not undergoing SN II explosions but rather causing "hypernovae" after the formation of a central black hole via core collapse. @ 2007 Published by Elsevier B.V.