This endeavor is a selective attempt to cover elemental abundances or estimates from the Big Bang to hydrostatic nucleosynthesis in stars and, finally, explosive nucleosynthesis. Apart from the theoretical aspects, we have attempted to include the experimental situation also, to get an overall picture. An effort is also made to link these with astronomical observations to highlight the topic's interdisciplinary nature and chalk out future directions. We have tried to include topics based on recent ideas, like using non-extensive statistics as probable solutions for the cosmological lithium problem -which technically can bring up connections with non-equilibrium statistical physics. The experiments with neutron-rich nuclei have also opened new vistas in nuclear physics. The influence that may have on abundance estimates is explored.