The central theme of the Epistle is God's righteousness revealed in Christ for our salvation (1:16,17). Righteousness is the basis of a faithful relationship between God and humanity. God Himself freely offers this living and growing relationship to all human beings, through Christ. St Paul shows this by discussing natural mortality, and the sinfulness of all ( 1:18-3:20), salvation through Christ alone, and not from the Law (3:21-4:25), new life in Christ through the sacrament of Baptism (5-7), new life in the Spirit through Chrismation (8), God's plan for Jews and Gentiles and their reconciliation in Christ (9-11), and finally Christian life in the Church and throughout the world (12-16).
The Apostle Paul's logic proceeds mainly from dichotomies ( two concepts are placed in opposition to each other ) and synergies ( two concepts work together ). Romans is certainly the most doctrinal, and logical epistles of Paul, and the only one he wrote to a church he had not yet visited.
St Paul highlights that a relationship with God transforms a Christian, empowering him or her to become the person intended by our Father in Heaven. A very important aspect of Romans ( and for Paul's letters in general ) is that 'there is no distinction between Jew and Greek; the same Lord is Lord of all and bestows his riches upon all who call upon Him.' (Rom 10:12)
For example we see in Rom 9:1-5 that St Paul is distressed about his Jewish kinfolk, as they concentrate on their Law and believe they can achieve righteousness and salvation through that alone. Christ fulfils this law, and it is through faith and love for Him that one is righteous and united with God. The Apostle explains later in the epistle (Rom 9:30-10:4) that the gentiles have managed to attain this righteousness as they have followed the Lord in faith - and of course gentiles were looked down upon by the Jews; but Paul is telling us here that no matter where we are from, we can all be one in Christ. For Paul, and the entire Church, the goal is for every human being to be saved, and to see his fellows fail to understand that the Θεάνθρωπος, and Saviour Christ has not come down on earth to 'abolish the law and the Prophets.. but to fulfil them.' (Matthew 5:17) The gentiles have their own problems, such as immoral behaviour, and the Jews have a false sense and understanding of righteousness - but Paul assures all groups that even though we all have our issues, through grace we can be reconciled to God and be one with Him in communion:
'So we, through many, are one body in Christ, and individually members one of another.' (Rom 12:5)