These lectures describe some aspects of the physics of massive neutrinos. After a brief introduction of neutrinos in the Standard Model, I discuss possible patterns for their masses. In particular, I show how the presence of a large Majorana mass term for the right-handed neutrinos can engender tiny neutrino masses for the observed neutrinos. If neutrinos have mass, different flavors of neutrinos can oscillate into one another. To analyze this phenomena, I develop the relevant formalism for neutrino oscillations, both in vacuum and in matter. After reviewing the existing (negative) evidence for neutrino masses coming from direct searches, I discuss evidence for, and hints of, neutrino oscillations in the atmosphere, the sun, and at accelerators. Some of the theoretical implications of these results are emphasized. I close these lectures by briefly outlining future experiments which will shed further light on atmospheric, accelerator and solar neutrino oscillations. A pedagogical discussion of Dirac and Majorana masses is contained in an appendix.

45 pages, 12 figures, Latex file, to be published in in The Proceedings of the VIII Escuela Mexicana de Particulas y Campos