This is a Phase 1/2 trial in two parts. Part A is a prospective, randomized, double-masked, vehicle controlled, paired-eye study in approximately 16 subjects to evaluate safety, tolerability and efficacy of elamipretide 1.0% topical ophthalmic solution in patients with Fuchs' Corneal Endothelial Dystrophy (FCED) presenting with mild to moderate corneal edema. Part B is a prospective, randomized double-masked, vehicle controlled study in approximately 11 subjects to evaluate safety, tolerability, and efficacy of elamipretide 3.0% topical ophthalmic solution in patients with FCED presenting with mild to moderate corneal edema.