This book covers the field of neutrino physics and astrophysics, providing an up-to-date presentation of the different research topics on the frontier of the field. It starts with a historical description to understand how the different aspects of our knowledge about the neutrinos evolved up to the present state. The main required elements of the Standard Model of electroweak interactions are introduced, and the different neutrino interactions and detection techniques are presented. We introduce the various ways to give neutrinos a mass and the phenomenon of neutrino oscillations which provides the main evidence for non-vanishing neutrino masses. We then consider the neutrinos produced in the Sun, what we have learned from them, and how they can also be useful to study our star. The geoneutrinos produced by the radioactivity in the Earth are discussed and the status of their detection is presented. We survey the neutrino production in the supernova explosions at the end of the life of very massive stars, what has been observed in SN1987A, and what could be learned from a future supernova or from the observation of the diffuse supernova neutrino background. We describe in detail the neutrino production by cosmic rays interacting in the atmosphere, the evidence for their flavor oscillations, and the oscillograms to describe their flavor change in terrestrial matter. The different mechanisms of production of high-energy astrophysical neutrinos and the observations achieved with the IceCube detector are presented, also discussing their flavor content by means of the flavor triangle. We then examine the cosmological neutrino background, its impact on Big Bang nucleosynthesis and on the CMB observations, with the associated bound on their masses and effective number. Finally, we review the basics of the leptogenesis scenarios, which provide an attractive explanation for the observed baryon asymmetry of the Universe.