This second volume contains results that are related to motivic integration, model theory and non-archimedean geometry in various ways, with an emphasis on the mutual interactions between these fields.

The scope of these results is quite large, ranging from motives and resolution of singularities for formal schemes to Arakelov geometry and exponential sums. Motivic integration is not explicitly visible in all of the chapters, but it is often lurking in the background. For instance, resolution of singularities for formal schemes is an important ingredient in the study of motivic integrals on formal schemes, and the structure of trees in ℤp is a combinatorial analog of the structure of the truncation morphisms between Greenberg schemes of different levels.

The primary aim of the second volume is to illustrate the rich interactions between motivic integration, model theory and non-archimedean geometry, and their influence on problems arising in various branches of mathematics. We hope that these results will bring the reader both enjoyment and inspiration.