As in other places, Paul seeks to establish the legitimacy of his authority by recounting his conversion and special calling by Jesus himself (v15-17). He begins his account in v10 with the significant point that he is not seeking to be a people-pleaser, but only a God-pleaser; Paul knows whom he serves! What seems strange at first is the fact that Paul makes a point of the fact that he spent minimal time with the other Apostles (v16-24). This is to highlight his uniquely direct commissioning from Jesus, giving him equal authority as the other Apostles. For if he was a disciple of the Apostles, his authority would merely be derivative of theirs.
The beginning of ch. 2 continues his testimony, but also begins to address the issue of Judaizers, pointing out that the other Apostles did not tolerate their false teaching either. Verses 4 & 5 make the strong condemnation “false brothers” upon the Judaizers, strong language that Paul often uses against anyone who opposes the gospel (such as in 1 Tim. 6:3-5, Acts 20:29).
Some particularly notable things here is the boldness that is afforded to Paul by his authority, and the idea that he and the other Apostles had complementary ministries (to the uncircumcised and the circumcised, respectively).