(Anders Nygren, Commentary on Romans. SCM: London 1952, p 15.)It is this total reorientation in the religious relationship which Paul, in the Philippian passage cited above [3:4-9], formulated with such definitive clarity, "not by my own righteousness which comes by the law, but by the righteousness which comes through faith in Christ, the righteousness from God."In that expression, “the righteousness from God,” the very foundation thought of the Epistle to the Romans is encompassed. That is affirmed by Paul himself when in 1:17 he states the theme for his letter. He does so with the following word, "The righteousness of God is revealed through faith for faith; as it is written, 'He who through faith is righteous shall live.'" And the whole epistle, as it proceeds, is nothing but a clarification of the contents of this "righteousness from God," and the consequences for the Christian life of the new righteousness of God which was revealed through Christ, and which is shared by him who believes in Christ.
Carson recommends Nygren for understanding the big picture of Romans and even though Nygren's commentary is over half a century old and originally translated from Swedish (!), it still presents the main ideas and structure of Romans in a lucid and careful style. I think Nygren's right, the overall purpose of the Apostle Paul in his letter to the Romans is to explain this righteousness that is from God.