Maximal subgroups of exceptional groups of Lie type,finite and algebraic

The maximal closed subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields are determined, subject to certain restrictions on the characteristic. This result is used to prove a reduction theorem for maximal subgroups of finite exceptional groups of Lie type: such a subgroup is either of known type, or it is almost simple. Finally, the generic almost simple maximal subgroups are determined for large characteristic.Dedicated to Professor J. Tits on the occasion of his sixtieth birthdaySupported in part by NSF and NSA grants and an SERC visiting fellowship at Imperial College, London.