The immediate purpose of the paper was neither to review the basic
definitions of percolation theory nor to rehearse the general physical notions
of universality and renormalization (an important technique to be described in
Part Two). It was rather to describe as concretely as possible, although in
hypothetical form, the geometric aspects of universality, especially conformal
invariance, in the context of percolation, and to present the numerical results
that support the hypotheses. On the other hand, one ulterior purpose is to draw
the attention of mathematicians to the mathematical problems posed by the
physical notions. Some precise basic definitions are necessary simply to orient
the reader. Moreover a brief description of scaling and universality on the one
hand and of renormalization on the other is also essential in order to
establish their physical importance and to clarify their mathematical content.