O-minimal structures and real analytic geometry

O-minimal structures Originate in model theory. At the same time this subject generalizes topics like semialgebraic and subanalytic geometry, and provides an efficient framework for developing Grothendieck's topologie moderee. No previous knowledge of the topic is assumed, and we include proofs of some basic o-minimal results. Next we indicate applications in several areas, and discuss various ways of building o-minimal structures on the real field. These structures are displayed in an inclusion diagram. We conclude with a list of open problems.