Reciprocity Laws have played an important role in the development of Number Theory. The expository article by Jared Weinstein in the Bulletin of the American Mathematical Society (2016) gives a technically sophisticated and commendable survey including fairly recent developments. The purpose of this lecture is to explain to a mathematician with little knowledge of algebraic number theory the origin of the problem, why reciprocity laws are interesting, and what some of the methods of the investigation and accomplishments are. Accordingly, the emphasis in the lecture will be somewhat different from those in standard accounts.

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