Sir Gawain is an alliterative poem in Middle English, attributed to an anonymous late fourteenth century poet. Basically,Tolkien did a modern English translation, with some introductory material. The story is fairly famous for those interested in Arthurian legends: at a New Year's feast at Camelot, a gigantic knight (the Green Knight) makes a challenge... but, well, I don't want to spoil it if you're going to read it.
Farmer Giles is Tolkien's own invented tale. Katheryn Crabbe once commented on the fairy story elements: 'Farmer Giles is the traditional fairy-tale hero. His heroic attributes are not obvious or conventional -- he is not braver or stronger, or wiser, or more handsome than other men -- but he is a hero nonetheless.' She adds that his virtues include prudence, discretion, reverence for the past, and wits.
Toss in a little luck for farmer Giles, and a dragon (for notable example), and you've got a delightful little tale with touches of Tolkien-style humor.