Baynes was an English artist who illustrated a landslide of works in an impressive variety of styles over the years. The turning point came from... well:
J.R.R. Tolkien had written Farmer Giles of Ham, a humorous novella about dragons and knight-errantry set in a faux-medieval period, but was dissatisfied with the work of the artist who had been chosen as illustrator. Baynes's work caught Tolkien's eye and she got the job, creating a lively set of pictures that wittily pastiche the look of illuminated medieval manuscripts. So perfectly did Baynes capture the essence of Tolkien's tale that he declared them to be "more than illustrations, they are a collateral theme". He also delighted in reporting that friends had said that her pictures had succeeded in reducing his text to "a commentary on the drawings"(!)
It seems Tolkien also wanted her to illustrate the Lord of the Rings books, but it was not to be. Just imagine the Hildebrandt brothers with serious competition, hey?
In any case, she did do a nice map for LotR:
Lots more of her art and life-story below, including more on her collaborations with Tolkien:
I like Farmer Giles of Ham, but my fave Tolkien story (non-Arda at least) is Smith of Wootton Major. Coincidentally, my favorite Neil Gaiman book is Stardust, which is a similar story of a boy exploring a fae realm. If you like Tolkien, or folk fantasy, read Tolkien's short stories
I remember a lot of them being in poem form, something I had to be in the right frame of mind to get in to. But I liked getting more backstory on Bombadil in particular.
Indeed, I kind of get a kick out of Tolkien fans arguing to this day what kind of being Bombadil was.