The classic work would be Marco Livio's "The Golden Ratio," which is widely available. If you search a few thrift stores in your area, you'll probably find a copy for a buck.
As interesting as that book is, I'd counsel you not to take "ratio" talk too seriously. Here is a good article explaining
why the ratio is not as big a deal in design as some people think. Here is a balanced look
at the debate between debunkers and believers. Also worth reading: "Lies and Debunked Legends about the Golden Ratio"
and this Skeptoid article
Be particularly wary about claims that Leonardo da Vinci used the ratio in all of his art, particularly in his famous drawing "The Vitruvian Man." While he certainly knew about the ratio -- he was, after all, closely associated with the geometer Luca Pacioli -- Leonardo was much more fascinated by what has been called the Silver Ratio, which relates to octagonal geometry. If you look at Leonardo's notebooks (which Golden Ratio buffs never do), you'll see that he had an obsessive interest in octagons throughout his career. The Vitruvian Man and the Last Supper are based on octagonal geometry. So is the de Ganay version of the Salvator Mundi, which my ladyfriend and I consider a product of Leonardo's studio at least partially painted by the master himself. This video
lays out much of our argument.