Dilatation structures I. Fundamentals

A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a structure allows to do analysis, in the sense of differential calculus, on a metric space. We also describe a formal, universal calculus with binary decorated planar trees, which underlies any dilatation structure.