In chapter one, Paul condemned (v9) the false teaching of salvation by law. He defended the gospel he taught was a direct revelation from the Lord Jesus Christ (v12).
Paul’s journey in his early years as believers
After Paul experience the vision of Jesus Christ on the road to Damascus (Acts 9:4), he some time in Damascus preaching the gospel (Acts 9:19,23). We are not sure exactly how long he stayed in Damascus, maybe few weeks. The Jews did not like what Paul was preaching and wanted to kill him (Acts 9:23), the believers at Damascus helped Paul to escape by lowering Paul in a basket through an opening in the city wall. (Acts 9:25).
Gal 1:17 tells us Paul went into Arabia and later returned to Damascus. The total time of that period in his life was three years. That means after Paul escaped from Damascus initially in Act 9:25, he traveled to Arabia, where he potential spend a lot of time reading the OT to discover Christ in the OT, and Christ revealed Himself through His words to Paul during these precious years. And then Paul return back to Damascus. There is a three years gap between verse 25 and verse 26 in Acts chapter 9.
After the three years in Arabia (and Damascus), Paul went to Jerusalem (Acts 9:26). The believers were afraid of Paul, not believing that he really was a disciple of Christ. But Barnabas took him and brought him to the apostles (Acts 9:27). Paul stayed with Peter for 15 days (Gal 1:18) and met James, the Lord’s brother (Gal 1:19). Paul again preached the gospel in Jerusalem to the Jews, and the Jews hated Paul and wanted to kill Paul. The brothers helped Paul to espace, the took him down to Caesarea in Syria, and sent him off to Tarsus (Acts 9:30), which is a city in Cilicia (Gal 1:21).
Paul potential has spent 13 years in Tarsus (Gal 2:1), until Barnabas went to Tarsus to look for Paul, and brought Paul to Antioch in Syria (Act 11:25-26). For a whole year, Barnabas and Paul met with the church and taught great numbers of people, there is when disciples were called Christians first at Antioch. (Acts 11:26).
Paul, together with Barnabas went to Jerusalem the second time (Gal 2:1, Act 11:30), to deliver gifts from the church of Antioch to the elders in Jerusalem to help them during the time of severe famine in Judea.