Albert Barnes on Romans 16:20

And the God of peace. The God who promotes peace, Rom 15:33.

Shall bruise. The language here refers to the prediction in Gen 3:15. It here means to subdue, to gain the victory over. It denotes Paul's confidence that they would gain the victory, and would be able to overcome all the arts of those who were endeavouring to sow discord and contention among them.

Satan. The word Satan is Hebrew, meaning, originally, an accuser, a calumniator, and then an enemy. It is given to the prince of evil spirits from his enmity to God and men. He is here regarded as the author of all attempts to promote discord in the church, by whomsoever those attempts were made. Hence they who attempt to produce divisions are called "his ministers," 2Cor 11:15. God would disappoint their malignant purposes, and promote the prevalence of peace.

The grace. The favour; the mercy, etc. The Lord Jesus is the Prince of Peace, (Isa 9:6 comp. Lk 2:14, Jn 14:27); and this expression is a prayer to him, or an earnest wish expressed, that the design of his coming might be accomplished in promoting the prevalence of order and peace. Comp. 1Cor 16:23, Rev 22:21.

(c) "God of peace" Rom 15:33 (2) "bruise" or, "tread" (d) "Satan" Gen 3:15 (e) "shortly" Rev 12:10 (f) "Amen" 1Cor 16:23, Rev 22:21