  This paper is the first in a sequence on the structure of sets of solutions
to systems of equations over a free semigroup. To describe the structure, we
present a Makanin-Razborov diagram that encodes the set of solutions to such
system of equations. In the sequel we show how this diagram, and the tools that
are used in constructing it, can be applied to analyze fragments of the first
order theory of free semigroups.
