Albert Barnes Commentary Acts 3:13

"The God of Abraham, and of Isaac, and of Jacob, the God of our fathers, hath glorified his Servant Jesus; whom ye delivered up, and denied before the face of Pilate, when he had determined to release him." — Acts 3:13 (ASV)

The God of Abraham. He is called the God of Abraham because Abraham acknowledged Him as his God, and because God showed Himself to be his Friend. (Exodus 3:6, 15; Genesis 28:13; Genesis 26:24).

It was important to show that it was the same God who had done this who had been acknowledged by their fathers, and that they were not about to introduce the worship of any other God. And it was especially important because the promise had been made to Abraham, that in his seed should all the families of the earth be blessed (Genesis 12:3). .

Has glorified. That is, God has honored him. You denied, despised, and murdered him; but God has exalted and honored him. This miracle was done in the name of Jesus (Acts 3:6). It was the power of God that had restored him. By putting forth this power, God had shown that He approved the work of His Son and was disposed to honor Him in the sight of men. (Ephesians 1:20–22; Philippians 2:9–11; Hebrews 2:9; Revelation 1:5–18).

You delivered up. That is, you delivered him to the Romans to be put to death.

And denied him in the presence of Pilate. You denied that he was the Messiah. You were unwilling to own him as your long-expected King (John 19:15).

When he [Pilate] was determined, etc. (Matthew 27:17–25; Luke 23:16–23). Pilate was satisfied of his innocence, but he was weak, timid, and irresolute, and yielded to their wishes. The fact that Pilate regarded him as innocent was a strong aggravation of their crime. They should have regarded him as innocent; but they urged on his condemnation, against the deliberate judgment of the one before whom they had arraigned him, and thus showed how obstinately they were resolved on his death.

(See also Revelation 1:5, 18). Regarding the phrase denied him, compare to John 19:15. The phrase let him go means “Release him.”