All 5 Uses

adieu
in
A Midsummer Night's Dream
(Auto-generated)

LYSANDER Helena, adieu: As you on him, Demetrius dote on you!†
Scene 1.1

adieu = goodbye
Take pains; be perfect; adieu.†
Scene 1.2 *
Tongue, not a word:— Come, trusty sword; Come, blade, my breast imbrue; And farewell, friends:— Thus Thisbe ends; Adieu, adieu, adieu.†
Scene 5.1
Tongue, not a word:— Come, trusty sword; Come, blade, my breast imbrue; And farewell, friends:— Thus Thisbe ends; Adieu, adieu, adieu.†
Scene 5.1
Tongue, not a word:— Come, trusty sword; Come, blade, my breast imbrue; And farewell, friends:— Thus Thisbe ends; Adieu, adieu, adieu.†
Scene 5.1

Definitions:

(1) (adieu)
a farewell remark (an alternative to goodbye)

Adieu is typically more formal than bye. It comes from the French, à Dieu which literally means "to God" — as in I entrust you to God's care.
(2) (meaning too rare to warrant focus)