Short answers, pulled from the story.
The Matter of Britain is the body of medieval literature and legendary material associated with Great Britain and Brittany, centered on King Arthur and the legendary kings of Britain. It was one of three major Western story cycles named by the 12th-century French poet Jean Bodel, alongside the Matter of France and the Matter of Rome. Its works, in prose and verse, flourished from the 12th to the 16th century.
The French poet Jean Bodel named all three in his 12th-century epic, the Song of the Saxons. The other two are the Matter of France, covering the legends of Charlemagne and his companions, and the Matter of Rome, drawn from classical mythology and classical history.
Geoffrey of Monmouth's Historia Regum Britanniae, written in the 12th century, is a central component of the Matter of Britain. Geoffrey drew on the 9th-century Historia Brittonum and other ancient British texts to construct a pseudo-historical origin story linking Britain to the Trojan War through the figure of Brutus of Troy.
The Vulgate Cycle, also known as the Lancelot-Grail Cycle, is a long 13th-century collection of interlacing Old French prose episodes covering the full arc of King Arthur's reign. It established many iconic elements of the Arthurian tradition, including the court of Camelot, the Holy Grail quest, and the relationship between Lancelot and Guinevere.
Le Morte d'Arthur is Thomas Malory's 15th-century compilation of Arthurian romance, drawn mainly from the French prose cycles. It established an English-language near-canon of the Arthurian tradition and remains highly influential today. The 19th-century Romanticist revival, particularly in Victorian Britain, spread Malory's telling around the world.
Major scholarly schools include the Celticists, who link Arthur and the Grail to Celtic mythology, and the mythologists, who read the tradition as allegory of spiritual development, with Joseph Campbell among the key figures. The ritualist school, led by Jessie L. Weston in her 1920 work From Ritual to Romance, traced Arthurian imagery to early nature worship, though that view is no longer fashionable. Newer approaches include C. Scott Littleton's Scythian and Sarmatian origins theory.