In this thesis we classify saturated fusion systems on ρ-groups S containing an extraspecial subgroup of index ρ for an arbitrary odd prime ρ. We prove that if F is a saturated fusion system on S with Op(F) = 1 then either |S|≤ ρ⁶ or S is isomorphic to a unique group of order ρ^ρ-1. We either classify the fusion systems or cite references to show that F is known in all cases except when S is a Sylow ρ-subgroup of SL₄(ρ) which remains as future work. When |S| ρ^ρ-1 with ρ≥11 we describe new infinite exotic families related to those constructed by Parker and Stroth.