Then after three years I went up to Jerusalem to see Peter, and abode with him fifteen days.
Note 8 at Ga 1:18: The mention of three years here is probably implying that three years after his conversion, he went up to Jerusalem (see note 1 at Ac 9:26). The reason for this visit was to get acquainted with Peter. He stayed with Peter for fifteen days.
There may be a couple of reasons that Paul mentioned this visit: (1) He was only with Peter a brief period of time and could not possibly have been instructed fully in the Gospel so quickly. The Judaizers were saying that Paul had learned his Gospel from the apostles and had now defected from its original message. This makes Paul's point that the Gospel was revealed to him not by man but by God (Ga 1:11). (2) The Judaizers could claim Paul's message was different than Peter's, and Paul wanted his readers to understand his acquaintance and harmony with Peter and James, the brother of the Lord (Ga 1:19), who was the overseer of the Jerusalem church.