In this talk (and the next one) I shall briefly describe a research plan that encompasses several topics from model theory and algebra. The motivation is this: Is there a motivic Tate formula? To explain this question I shall touch on several things: adelic structures over valued fields and Tate's thesis (this talk), Weispfenning's first-order approach to adelic structures, and finally Hrushovski and Kazhdan's integration theory of valued fields. To explicate any one of these topics requires a great deal more time than an hour. So my presentation will be very informal and oriented to the "big ideas" rather than correctness.