Galatians 1:20

Now the things which I write unto you, behold, before God, I lie not.

Paul solemnly declares before God that his written account of his history, personal experience, commission, visits and movements is true and he is not lying. The account he so confirms proves that the gospel he preached was given him directly by revelation of Jesus Christ in him and taught to him by no person, so there is but one gospel. In calling God as witness to confirm the truth of what he writes about his commission and experience he makes a solemn oath. That appeal has the essential features of a lawful judicial oath, voluntarily made, and as an oath of truthful testimony it does not violate the third commandment and is not profanity.

Paul's Truthful Testimony

Before God Paul solemnly declares that the written account of his history is true and he is not lying, confirming his personal experience, commission, visits and movements. He calls God as witness that what he has written concerning his commission and experience is the truth.
The account so affirmed proves that the gospel he preached was given him directly by revelation of Jesus Christ in him, not taught to him by any person or any human teacher, so there is but one gospel, namely that which Paul preached.
After the Lord met him near Damascus he conferred not with flesh and blood but went into Arabia and returned to Damascus, first preaching there and in the regions around Damascus the gospel he had received. He did not receive teaching from the Jewish Christians after his conversion.
After three years he went up to Jerusalem and stayed fifteen days, seeing no apostles except James the Lord's brother, then went into the regions of Syria and Cilicia while remaining unknown by face to the churches in Judea. Those churches knew him only by report as the former persecutor who now preached the faith he had once tried to destroy, and God was glorified in him.
The chapter records Saul's conversion and traces his movements and ministry during the first sixteen to seventeen years of his Christian life before he preached to the Gentiles and before the church sent out her first missionaries. It proves he was not in connection with brethren by whom he could have been biased, and the narrative continues without break into chapter 2. The chapter recounting his early history and first visit to Jerusalem is to be reviewed with Galatians 2:1-5 to fix clearly in mind the incidents of the meeting in Jerusalem fourteen years after the first visit that establishes the teaching of no respect of persons in Galatians 2:6-10.
He later communicated to the apostles in Jerusalem the same gospel he had already preached, so his preaching to the Gentiles did not introduce a new moral law.

Lawful Solemn Oath

The declaration calls God as witness to confirm the truth of what is written about commission and personal experience, and that calling makes the statement a solemn oath. The appeal affirms before God that there is no falsehood in the written account, solemnly invoking Him to attest its truthfulness.

The appeal contains the essential features of a judicial oath and is of the same kind as the appeal to God made in a lawful judicial oath. It is made voluntarily, and as such it stands as an example of judicial swearing.

As an oath of truthful testimony given for the benefit of future generations, it does not violate the third commandment and is not profanity. The appeal itself carries the penalty for speaking falsely within it by implication, even though no penalty is expressly stated.