A deeper understanding of neutrinos, with the goal to reveal their nature and exact role within particle physics, is at the frontier of current research. This book reviews the field in a concise fashion and highlights the most pressing issues and areas of strongest topical interest. It provides a clear, self-contained, and logical treatment of the fundamental physics aspects, appropriate for graduate students. Starting with the relevant basics of the SM, neutrinos are introduced, and the quantum mechanical effect of oscillations is explained in detail. A strong focus is then set on the phenomenon of lepton number violation, especially in 0nbb decay, as the crucial probe to understand the nature of neutrinos. The role of neutrinos in astrophysics, expected to be of increasing importance for future research, is then described. Finally, models to explain the neutrino properties are outlined. The central theme of the book is the nature of neutrino masses and the above topics will revolve around this issue.