The Apostle Paul’s argument in Romans 3:21-4:25 can be seemed up in three words; Righteousness, Justification, and Faith. Romans 3:21-26 covers the universal provision of righteousness; Romans 3:27-31 covers justification and the purpose of the Law; and Romans 4:1-25 covers justification and Old Testament.
In Romans 3:21- But now apart from the Law the righteousness of God has been manifested, being witnessed by the Law and the Prophets- Paul gives the thesis for his argument. The Apostle Paul defines righteousness (the process by which God acts to put people in a right relationship with Him.) in verse 21. In Romans 3:21, Paul argues from God’s glory to prove that justification must be expected only by faith in Christ’s righteousness; there is no justification by the works of the law. There is another way laid open for man, the righteousness of God without the law is manifested now under the gospel. Justification may be obtained without the keeping of Moses’ law and this is called the righteousness of God, righteousness of his ordaining, and providing, and accepting.
Paul builds his case by building on his introduction to the idea of justification by faith in Romans 1:17. The verses that follow Romans 3:21 contain important theological ideas: the righteousness of God, justification, the shift in salvation history, faith, sin, redemption, grace, propitiation, forgiveness, and the justice of God. Paul concludes that that Law of Moses (or works of man) cannot save anyone; it is the faith in Christ that saves man from our sins. In Romans 3:21-4:25, Paul establishes the need for righteousness for all people, he demonstrates its provision (3:21–5:11). First, it has been revealed through the faithfulness of Jesus Christ, being granted to all who put their trust in him (3:21-26). Second, the favor of God through faith is the same for all (Jew and Gentile alike) because God is One (3:27-31). Third, Paul backs up this astounding assertion with proof from the life of Abraham (4:1-25) since Abraham is seen to be father both of the Jews and of the Greeks—that is, he is a type of those who are saved by faith. This is illustrated by evidence that Abraham was not justified by works (4:1-8), nor by circumcision (4:9-12), but exclusively by faith in the promises of God (4:18-25). So too his spiritual offspring are justified by faith rather than by law (4:13-17, 23-25). Thus Abraham is seen to be the universal forefather of all believers, whether Jew or Greek.
Paul’s conclusion that faith and not works saves man may seem to go against what James writes in his letter; James 2:14-26. James most likely refers to vindication before men after one’s actions are seen, while in Paul refers to forensic declaration of innocence before God. James is mere intellectual assent (“even the demons believe and shudder” [James 2:19]), while for Paul it is a full embracing of the Savior as the only way in which one can escape damnation. James is works of mercy and is a necessary response of the believing heart; in Romans 3 are works of the Law as a means to obtaining salvation and, as such, are flawed and powerless. Finally, the appeal to the life of Abraham shows that for both Paul and James faith is an essential. James argues that Abraham’s faith was seen in his works; Paul argues that Abraham’s faith makes him the father of both Jews and Gentiles (Romans 4), since faith is a constituent element in saving faith prior to Abraham’s circumcision as well as after.
 Allan Ross, “Justification (Romans 3:21—4:25),” Bible.org, August 5, 2004. https://bible.org/seriespage/justification-romans-321%E2%80%94425
 Douglas J. Moo, The New Application Commentary: Romans. (Grand Rapids, MI: Zondervan, 2000), 126.
 Matthew Henry, “Matthew Henry Commentary on Romans,” Biblegate.com, N.A. http://www.biblestudytools.com/commentaries/matthew-henry-complete/romans/3.html
 Douglas J. Moo, The New Application Commentary: Romans. (Grand Rapids, MI: Zondervan, 2000), 125.
 Daniel B. Wallace, “Romans: Introduction, Argument, and Outline,” Bible.org, June 24, 2004. https://bible.org/seriespage/romans-introduction-argument-and-outline
 Daniel B. Wallace, “Romans 3:28 and Jas 2:24: A Comparison,” Bible.org, October 6, 2009. https://bible.org/article/romans-328-and-jas-224-comparison