Certain ideals in L1-algebras.- The property P1, applications.- Some properties equivalent to P1. Relativization.- Segal algebras.- Examples.- Approximate units in Banach algebras: definitions.- Approximate units in Banach algebras: lemmas.- Approximate units in Segal algebras.- Some general results on Segal algebras.- Certain ideals in Segal algebras.- Canonical representation of the ideals.- Segal algebras and normal subgroups.- Segal algebras on quotient groups.- Closed ideals with approximate units in Segal algebras.- Symmetric Segal algebras on compact groups.- Segal algebras on abelian groups.- L1-algebras of compact and of abelian groups.