Does abelian imply normal?

Excuse me, but I've been pondering over this mathematical concept and I'm a bit confused. Can you clarify for me if the term "abelian" inherently implies that a group is also "normal"? It seems like there might be some overlap in properties, but I'm not entirely sure. Could you please explain the relationship, if any, between these two concepts in simple terms? Thank you for your time and assistance.