  We prove a Jordan decomposition theorem for minimal connected simple groups
of finite Morley rank with non-trivial Weyl group. From this, we deduce a
precise structural description of Borel subgroups of this family of simple
groups. Along the way we prove a Tetrachotomy theorem that classifies minimal
connected simple groups. Some of the techniques that we develop help us obtain
a simpler proof of a theorem of Burdges, Cherlin and Jaligot.
