In this lecture I shall introduce the notion of an o-minimal Tarski system and briefly describe how it usefully generalizes the concept of semi-algebraic and, indeed, subanalytic set. No model theory will be assumed! Since there do exist excellent survey papers in this area, notably those of van den Dries, I shall keep these remarks to a minimum and my main emphasis for the rest of this lecture and the series will be on examples and methods for establishing the o-minimality of a given system of sets in real Euclidean space.