A law is a standard of conduct. The word law appears 72 times in Romans. About 70% of the time the Old Testament law is indicated via the article "the" or the context. Paul also uses this word in a broader sense, meaning a body of rules that govern conduct.
Romans 3 Outline
Objections to God's righteousness answered
God is faithful
God is just
Everyone is guilty of sin.
All humanity is unrighteous
Guilty in motive, deed, and word.
Destructive lifestyles of evil
Lacking reverence toward God
Purpose of the law
Righteousness of God
Lost condition of mankind
Redemption in Christ
Justification by faith
Justification is acquittal from sin. It is the opposite of condemnation (Rom 5:16-18). Justification is not meritoriously earned by good conduct (Rom 3:20). Rather, God grants justification by his grace as a free gift (Rom 3:24, 8:33). We obtain access to God's grace by faith (Rom 5:2).
Jesus was crucified for our sins, and raised for our justification (Rom 4:23-25). God views a justified person as without sin, not because that person is sinless (Rom 3:23), but because God honors the sacrifice of Christ.
Jesus' righteousness is imputed to the sinner, clearing that Christian from the penalty of sin. This justification by faith results in peace (Rom 5:1).
Faith and Works
James related works to faith in James 2:14-26, writing that "faith without works is dead" and "a person is justified by works and not by faith alone" (2:17, 2:24).