In Sir Gawain and the Green Knight, though the story begins in Arthur's court at Christmas time when a mysterious stranger enters the hall and issues an open challenge, the core of this story is about Sir Gawain and the kind of man he is.
When the Green Knight issues an invitation for any man to have the first free swing at him with an axe, Gawain takes the challenge believing he will easily win. However, when the Green Knight picks up his head and continues to speak, he reminds the stunned Gawain to meet him at the Green Chapel to settle this challenge in one year's time, where the Green Knight will get the chance to take his swing on Gawain.
Gawain is an honorable man. Though he does not want to go as the next Christas season approaches, he does so—because he gave his word— arriving at a castle near the Green Chapel a little early. The master of the keep, Bertilak, invites Gawain to spend the holidays with them. During this time, Bertilak says they will share a portion of what each receives every day. So while Bertilak goes out to hunt, his wife tries to seduce Gawain. Except for keeping the magic belt she gives him and the knowledge of its presence on his body a secret, he avoids the advances the lady of the castle makes and remains honorable to his agreement to Bertilak.
When they finally meet, the Green Knight (actually this is Bertilak) admits that he was testing one of Arthur's knights to see if he was as honorable as the knights in Arthur's court were reputed to be. Even while testing Gawain with the axe, but not killing him (and he brings the axe down three times), Gawain is a man of his word, prepared to die in accordance with his vow. Bertilak is impressed with Gawain and releases him from their agreement.
If I were to write a critical paper on this epic, I believe I would write it about how honorable and dedicated Gawain is—the model of a true Arthurian knight—which he proves to Bertilak through his actions. I would support this theme with specific examples that prove Gawain's sense of honor in keeping up his end of the bargain to return to meet the Green Knight, and all he does to resist temptation while at Bertilak's house. (Don't forget he is not perfect: he keeps the gift of the belt a secret—and Bertilak knows this—but Bertilak/the Green Knight does not fault him for it.) Good luck with the paper.
A fascinating Middle English romance, Sir Gawain and the Green Knight, is believed to be a major work belonging to the "Matter of Britain", and a landmark of the "Alliterative Revival" of the 13th century.
The poem is an allegorical account of the Christian knight Sir Gawain's quest in the form of an absorbing narrative that describes his journey from King Arthur's capital, Camelot, to the Green Chapel of the mysterious Green Knight, the latter representing a vegetation god owing its origin to the pagan muthology and folkloric ceremony.
The story commences from King Arthur's court where the Green Knight appears with a challenge: a beheading game. The Green Knight challenges the knights of Arthur's round-table to behead him with the axe that he himself bears. Sir Gawain accepts the challenge and beheads the Green Knight. He must visit the Green Chapel within a year to receive the blow back from the Green Knight. After a lapse of one year, Sir Gawain sets out on his journey to the Green Chapel, and passes through an ordeal of seduction at the castle of Lord Bertilac. As Sir Gawain at last reaches the chapel, he finds that the Green Knight is none but Lord Bertilac. The Green Knight gives a nick at the third attempt on Sir Gawain's shoulder as a punishment. The Christian Knight returns to Camelot and all the Round Table knight wear a Green Badge as token of the mission.