Are all abelian groups normal?

Excuse me, but I'm a bit confused about the concept of abelian groups and their normality. Could you please clarify if all abelian groups are inherently normal, or is there a specific condition or context in which this assertion holds true? I understand that abelian groups possess the commutative property, but I'm not entirely sure how this relates to the concept of normality in group theory. Your insights would be greatly appreciated.