PASSAGE: "We ourselves, who are Jews by birth and not Gentile sinners, yet who know that a man is not justified by works of the law but through faith in Jesus Christ, even we have believed in Christ Jesus, in order to be justified by faith in Christ, and not by works of the law, because by works of the law shall no one be justified" (Galatians 2:15-16 RSV).
COMMENT: You ask for an interpretation of all of Galatians, which I am not able to do in one response. Instead, I chose the passage above which emphasizes one of Paul's key teachings in this letter—and, indeed, in his entire ministry.
This is a section of a speech which, Paul tells the Galatians, he made to Peter (Cephas) in Antioch. At issue was the urgent question of whether the gentiles Paul was converting to belief in Jesus Christ had to first become Jews—and undergo circumcision—before being accepted into the fellowship of The Way. Peter and the church in Jerusalem that he represented at this time were convinced that they did. Paul insists that "if justification were through the law, then Christ died to no purpose" (Galatians 2:21). The purpose of the law, to Paul, was to guide us to the point at which we are ready to understand and embrace the spiritual truth that Jesus taught and demonstrated: our innate Oneness with the Divine. Once we accept that truth, obedience to the law is no longer necessary. In essence, Jesus “fulfilled” the law through his message and demonstration. We don't “earn” our way into the new consciousness that Jesus describes as the kingdom of heaven by meticulously obeying the dictates of the law, but by embracing our spiritual truth.