These lecture notes are based on material presented at the Sixth Mexican School of Nuclear Physics, they introduce the reader into various topics including theoretical models and algebraic techniques used to describe the nucleus; concepts of interaction of the radiation with matter that are important to understand the way detection systems works; acceleration techniques and their application to different research areas in science; research with radioactive ion beams a powerful new technique that is pushing the frontiers in nuclear physics; theories of stellar evolution and nucleosynthesis; and recent measurements of neutrino mass and mixing.