Verse Quran
33:4 Allah has not made for any man two hearts in his (one) body: nor has He made your wives whom ye divorce by Zihar your mothers: nor has He made your adopted sons your sons. Such is (only) your (manner of) speech by your mouths. But Allah tells (you) the Truth, and He shows the (right) Way.
33:5 Call them by (the names of) their fathers: that is juster in the sight of Allah. But if ye know not their father's (names, call them) your Brothers in faith, or your maulas. But there is no blame on you if ye make a mistake therein: (what counts is) the intention of your hearts: and Allah is Oft-Returning, Most Merciful.
33:37 Behold! Thou didst say to one who had received the grace of Allah and thy favour: "Retain thou (in wedlock) thy wife, and fear Allah." But thou didst hide in thy heart that which Allah was about to make manifest: thou didst fear the people, but it is more fitting that thou shouldst fear Allah. Then when Zaid had dissolved (his marriage) with her, with the necessary (formality), We joined her in marriage to thee: in order that (in future) there may be no difficulty to the Believers in (the matter of) marriage with the wives of their adopted sons, when the latter have dissolved with the necessary (formality) (their marriage) with them. And Allah's command must be fulfilled.

The Quran's Verse about adoption

children, marriage, companions of the wood, job, wicked, usury, poverty, divining arrows, rebellious, bestow, rise of morn, mischief, conquest, fatwa, booty, ransom, fisk, creation, booty, unseen,