Abstract
This is the first of a pair of papers devoted to the local invariants of
Goursat distributions. The study of these distributions naturally leads to a
tower of spaces over an arbitrary surface, called the monster tower, and thence
to connections with the topic of singularities of curves on surfaces. Here we
study those invariants of Goursat distributions akin to those of curves on
surfaces, which we call structural invariants. In the subsequent paper we will
relate these structural invariants to the small-growth invariants.