In Book 3 we get back to what most people would think of as “core” King Arthur: the founding of the Round Table. Arthur has won his early wars, and everything is going fine, but his barons are on his case about getting married; possibly they don’t want another Uther situation, and the kingdom without an heir. Arthur has his heart set on Guenever, daughter of King Leodegrance (whom Arthur and his Continental allies delivered from a siege back in Book 1). Despite Merlin’s warning that she won’t be faithful, Arthur’s mind is made up.
There are several versions out there of where the actual Round Table came from; in this one, it belongs to Leodegrance, who was given it by Uther and now gives it (back) to Arthur as a wedding gift along with 100 knights. The Round Table seats 150, so Merlin goes out looking for 50 more to make up the shortfall, but he can only find 28. Every seat has a name except two, so we are left looking for 20 knights as the wedding festivities start.
Malory loves numbers.
The only one actually added to the Round Table here is Pellinor, but two other notable knights are created at the same time: Sir Tor, putative son of a cowherd, actually son of Pellinor, who raped his mom, and Sir Gawaine, already plotting revenge against that same Pellinor on account of having killed his father Lot.
There follows the wedding, and the Adventure of the White Hart. Gawaine, Tor, and Pellinor are each assigned a quest by Merlin to bring back a white hart, a dog and a knight, and a lady and another knight, respectively.
Gawaine’s quest doesn’t go well at all (he comes off terribly in Malory as a rule; I always have to go and reread The Green Knight afterward). He fails to show mercy when he should have, and accidentally kills a lady, and is thereafter required to be particularly solicitous of them in his future career. Tor has a nice successful little adventure, which is as a consequence rather dull.
Pellinor’s adventure is complicated, and his overall success is marred because at its outset he ignores a woman crying for help for her wounded lover, and both of them die. Merlin later tells Pellinor that the woman was his own daughter (Pellinor has more random kids than anyone else in this book), and Pellinor will be betrayed by someone he trusts as a result.
Arthur hands around some post-nuptial largesse. All of the knights promise not to do murder or treason or cruelty, to be merciful, to always protect ladies, and not to take part in wrongful quarrels. They frequently fail in these promises in the books to follow, especially that last one, and while there are kinda-sorta consequences sometimes, there isn’t a strong moral flavor to most of these tales (except the Grail quest, which is quite a different animal from the rest of them).