Arthurian Folklore: An Introduction.

"He hardly more than touched the sword" - illustrated by Walter J. Enright

King Arthur and His Knights (1903) by Maude L. Radford

King Arthur is a legendary figure of British folklore. Possibly based on a real man (Lucius Artorius Castus, Riothamus, etc.), the character has been reimagined from the medieval era to the present. He's also had a legion of characters crop up around him. With centuries of major and minor works across written and visual media, newcomers to the Arthurian mythos may not know where to begin. Here are a few recommendations.

Primary texts:

"Culhwch ac Olwen" a Welsh tale where Arthur helps his cousin get a wife.

"The Dream of Rhonabwy" a Welsh tale where Arthur plays cards while a battle rages.

"The Companionship of Myrddin and Gwenddydd his Sister" a Welsh poem featuring Merlin.

"Tom A Lincoln" an English romance starring Arthur's illegitimate son.

"The Jeaste of Sir Gawain" an English tale where Gawain seduces a woman, offending her kinsmen.

The Romance of Arthur: An Anthology of Medieval Texts in Translation, 3rd Edition (2013) by Norris Jay Lacy & James J. Wilhelm.
A collection of Arthurian narratives from Welsh, French, Norse, German and Latin traditions.

Lancelot–Grail: The Old French Arthurian Vulgate and Post-Vulgate in Translation (1992 - 1996) by Norris J. Lacy.
A multivolume translation of one of the most important Arthurian narrative cycles.

The Portuguese Book of Joseph of Arimathaea (2017) by Henry Hare Carter.
A study of an intermediate text that links the death of Jesus Christ with later adventures of Arthur's knights. The actual story can be read in English here.

Scholarship:

The Camelot Project 
A database for all things Arthuriana. Includes archived interviews, artwork, and English translations of many texts.

An Index of Themes and Motifs in Twelfth-Century French Arthurian Poetry (1992) by E. H. Ruck.
A comprehensive listing and description of the small narrative elements in Arthurian poems.

Index des motifs narratifs dans les romans arthuriens français en vers: XIIe-XIIIe siècles (1992) by Anita Guerreau-Jalabert.
Same as the above but for Arthurian prose.

From Scythia to Camelot by C. Scott Littleton and Linda A. Malcor (2000)

A book which argues against the supposed Celtic origins of the Arthurian mythos. It claims that the Holy Grail legends derive from the Iranians.

King Arthur in Antiquity (2004) by Graham Anderson.
Same as the above except it proposes an ancient Greco-Roman origin.