The Cowper and Newton Museum has a brief but correct article on the origin of "Amazing Grace" on their website pages. Amazing Grace
The curate of Olney Church (c. 1772) took as his text the opening words of David's Prayer in 1 Chronicles chapter 17. Then he explained how David came to that point in his life. "And all of that to one so insignificant, so unworthy."
"Reflecting upon the preserving grace of God to him in his turbulent seafaring days, Newton wrote a poem for that meeting to illustrate the gist of his message. He called it 'Of Faith's Review and Expectation.'
The six verses are the same as those in "The Olney Hymns" published in 1779, hymn 41, 1Chr 17:16, 17. Genie posted them 13 Sept. 02 in this thread (One error- the letter b is mis-set as h in but, verse 1, line 3).
The Table of Contents to "Olney Hymns" is here: Olney Index