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The existence of neutrinos -- neutral, massless, almost- noninteracting counterparts of the electron -- was first proposed in 1930, in response to apparently incomprehensible experimental results. Neutrinos have been a puzzle ever since! One indicator of their importance is the unusually large number of Nobel prizes awarded for neutrino work, the most recent in 2002. A brief account of the neutrino story will lead to a discussion of current issues in neutrino physics, including the intriguing possibility that neutrino interactions explain the existence of all matter in the universe. Techniques for the future study of neutrino physics will be described.