It is not 100% certain if Paul was writing this letter to just the Gentile Christians in Rome or just the Jewish Christians in Rome or both. There is evidence for both so many have concluded that he probably wrote this letter to both Jewish and Gentile Christians in Rome. It is also believed that the Jewish Christians living in Rome started this Church (possibly after Pentecost) and as the Gospel was made available to Gentiles through the teaching of Paul (throughout Asia and surrounding areas) they became part of this body. Some have suggested that there was a slight tension between these Jews and Gentiles in Rome so this letter was intended to bring unity to these two groups.
The letter of Romans has been described as the fullest extent of Paul’s theology but certainly not necessarily his complete theology. There are many themes throughout this letter so it is difficult to pinpoint one in particular. If I had to choose one theme it would be “the Gospel”.
The ESV Study Bible says, “A closer look at Romans reveals another purpose as well. Paul wanted the Christians in Rome to rally around his gospel so that Rome would become the base of operations by which he could proclaim the gospel in Spain (15:22–24). If Roman Christians did not agree with Paul's gospel message, especially on the issues being debated among Jews and Gentiles, then they would not support his proposed mission to Spain. Paul needed to explain the gospel in some detail so that the Christians in Rome would become the base from which he could proclaim the gospel in new regions.”
Paul had never been to Rome. The book of Acts tells us that Paul does eventually make it to Rome, but as a prisoner (He appeals to Caesar) who was free to roam (pun intended) and preach the Gospel.
  Moo, Douglas: The Epistle to the Romans. Grand Rapids, MI/Cambridge UK: William B. Eerdmans Publishing Company, 1996, p. 4