Paul introduces himself as a servant of Christ Jesus, an apostle set apart for the gospel of God. That gospel was promised in the writings of the prophets and concerns God's Son: a descendant of David according to the flesh and declared Son of God in power by his resurrection from the dead. Through him Paul received the task of calling all the nations to the obedience of faith, and the believers in Rome are among them, so he greets them with grace and peace.
He then thanks God that the faith of the Romans is known throughout the world, assures them that he prays for them constantly and explains that he longs to see them in order to strengthen them and be encouraged together with them. He calls himself a debtor to Greeks and barbarians, to the wise and the foolish, and he is eager to preach the gospel in Rome too.
Verses 16 and 17 give the thesis: Paul is not ashamed of the gospel, because it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. In it the righteousness of God is revealed from faith to faith, just as the prophet Habakkuk said: the righteous shall live by faith.
From verse 18 Paul shows why that salvation is needed. God's wrath is revealed against the ungodliness and unrighteousness of people who suppress the truth by their wickedness. What can be known about God is plain in creation, so no one has an excuse. Even so, people did not honor him or give thanks, exchanged the glory of God for images and worshiped what was created instead of the Creator. Three times the text says that God gave them up: to impurity, to dishonorable passions and to a debased mind. The chapter ends with a long list of evils and the warning that many not only practice them but approve of those who do.