Today we read Acts 3-28 and Romans 1-8. I am going to focus on Paul's three Missionary Journeys in Acts (though there were four or more if you consider his imprisonment), and will give a brief explanation for the background and purpose of Romans the Epistle.
Paul, led by the Spirit, went on several missionary journeys throughout the region to plant churches. After Paul became a Christian (Jesus having visited him, blinded him, and guided him to lordship), Paul and Barnabas were ordained by the brothers in Acts 13, and depart on their first journey. Accompanied by John Mark, they traveled from Antioch to Seleucia, then to Salamis on Cyprus (which is also the birthplace of Barnabas (Acts 4:36)). After preaching, they go to the other side of Cyprus to Paphos. After thier time in Paphos, they all travel to Perga and John Mark leaves to return to Jerusalem, an action later disapproved by Paul (Acts 15:36-41).
After Perga, they travel to Antioch in Pisidia (a different Antioch than where they began in Syria).
After Antioch, they traveled to Iconium, where they are forced to flee to Lystra due to a threat to their lives.
In Lystra, they are treated like Greek gods because Paul healed a man that was crippled. (Acts 14:6-10). Later, Jews from Pisidian Antioch and Iconium (the two locations prior to Lystra) arrive in Lystra and turn everyone against Paul and Barnabas, which leads Paul and Barnabas to be stoned. They even drag Paul's dead body to the outskirts of the city, but he still goes back to the city later to preach.
Then they went to Derbe, and afterwards go back through each city to strengthen the disciples. Ultimately, they return to Antioch, where they stay for ~three years. (Acts 14:26-28).
In Acts 15, Paul, Barnabas, Titus, and others are summoned to Jerusalem for a private meeting with James, Peter, and John (The Jerusalem Conference/Council) where they discuss the problem of Gentile Circumcision. After agreeing that circumcision is not necessary in order for the Gentiles to be saved, they write a letter that was to be delivered to the Gentile Churches describing the question of circumcision.
Paul then takes Silas with him to Tarsus and then to Derbe and Lystra (two places he already went with Barnabas on his first journey). Meanwhile, Barnabas takes John mark on a different journey entirely. In Lystra, they meet Timothy, and Timothy joins them on their journey.
After Paul has Timothy circumcised (contact me for more on this), they go with Silas to Galatia (Iconium) and Phrygia (Antioch). Interestingly, the Spirit forbids him from traveling into Asia following this, though Paul wanted to go.
Instead, Paul went to Mysia, then to Troas. Luke joins Paul on his journey in Troas. After receiving a vision of a man in Greece, they all travel together to Samothrace then to Neapolis. Afterwards, they go to Philippi (which is when Lydia is baptized- Acts 16:12-15). Paul and Silas are also arrested after casting a demon out of a female slave, but the Spirit frees them with a miraculous earthquake, and the prison guard is then converted.
Then, Paul and Silas go with Timothy and Luke to Amphipolis and Apollonia, arriving in Thessalonica, which is when Paul explains the Gospel for three weeks subsequent on the Sabbath.
Then Paul and Silas go to Berea, which is where we are shown the "great eagerness" of the Bereans (Acts 17:11-12). Paul travels alone to Athens, while Timothy and Silas stay for a time in Berea.
Paul, of course, preaches the gospel in Athens as he waits for his friends, Timothy and Silas. Paul preaches to the Greeks in Athens using Epicurean and Stioc philosophy. This is indicative of Paul's "all things to all men" philosophy, one we can all learn from.
From Athens, Paul goes to Corinth and meets Priscilla and Aquila. He stays in Corinth for over one year, and Timothy and Silas finally join him again (Acts 18:18). Later, Priscilla and Aquila accompany him to Ephesus and then to Caesarea and Jerusalem-- then finally, back to Antioch.
From Antioch, Paul goes back to Galatia and Phrygia to strengthen the churches (Acts 18:23). Afterwards, he goes to Ephesus for over three years, which is where he writes 1 & 2 Corinthians.
After the three years is up, Paul goes to Macedonia and Troas, and arrives in time for the Feast of Unleavened Bread (Acts 20:6). One night when he was preaching, a man fell asleep at the window and falls to his death. Paul goes to the man and brings him back to life (Acts 20:7-11).
Luke comes from Philippi to join Paul in Troas at this time, where they go to Assos and take a ship to Mitylene. From there, they travel past the islands of Chios and Samos and stay in Trogyllium for a night. Finally, they get to Miletus (Acts 20:15). In Miletus Paul asks the Ephesian Elders to visit him.
Paul finally boards for sail in Miletus, going to Cos and Rhodes (islands) and arrived at Patara, then Tyre, then Ptolemais, Caesarea, then finally Jerusalem (Acts 21:12-15).
It is around this time in 58 A.D. that Paul becomes a Roman prisoner in Caesarea.
Paul wrote the book of Romans from the city of Corinth during his third Journey. His purpose for writing the letter is to illustrate the doctrine of Christian faith as well as an approach to healthy Jewish/Gentile relationships. Romans also addresses important issues about faith, righteousness, and God's grace in Christ. Paul talks about righteousness being something not earned by merit but received by faith and grace. Righteousness can only be attained through faith and by Christ's atonement on the cross, a doctrine made explicity clear in Romans.
While a very short summary of Romans, I hope a helpful one to concisely explain the whole book in a short paragraph.