What is the doctrine of adoption?

The term "adoption" appears in the King James Version (KJV) of the Bible in the following verses:

Romans 8:15: "For ye have not received the spirit of bondage again to fear, but ye have received the Spirit of adoption, whereby we cry, Abba, Father."

Romans 8:23: "And not only they, but ourselves also, which have the first fruits of the Spirit, even we ourselves groan within ourselves, waiting for the adoption, to wit, the redemption of our body."

Galatians 4:5: "To redeem them that were under the law, that we might receive the adoption of sons."

These verses, particularly in Romans, discuss the believers' adoption into the family of God through the work of the Holy Spirit.