"Amazing Grace" is a great hymn. We sang it at my wedding, because it's distinctively Christian but non-Christians are still comfortable singing it. The story behind is is also great, and I've heard preachers summarize it a few times: slave trader John Newton converts to Christianity, repudiates slavery, and writes "Amazing Grace" to express his remorse and celebrate God's grace. That summary is technically true, but it doesn't do justice to the story.
Most importantly, that summary obscures the fact that John Newton remained involved in the slave trade for many years after his apparent conversion. It wasn't immediately obvious to him that his occupation was incompatible with his Christian commitments --- no doubt partly because his livelihood depended on it not being obvious. Clearly, though, over time he came to completely repudiate slavery and see his former career as a dire sin. His wretched personal history made him acutely aware of God's grace and made him an influential advocate for abolition.
There are many other interesting details. As a young seaman he was so ill-disciplined he was, incredibly, punished for excessive profanity. For eighteen months he was practically enslaved himself in West Africa. He went through several cycles of drawing near to God and relapsing into terrible sins. It's a long story of a great sinner gradually becoming a great saint.