Model theory has made substantial contributions to semialgebraic subanalytic p-adic rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases (such as the latter) it is the most abstract aspects of model theory which are relevant. This book originally published in 2000 arising from a series of introductory lectures for graduate students provides the necessary background to understanding both the model theory and the mathematics behind these applications. The book is unique in that the whole spectrum of contemporary model theory (stability simplicity o-minimality and variations) is covered and diverse areas of geometry (algebraic diophantine real analytic p-adic and rigid) are introduced and discussed all by leading experts in their fields. Language: English