What is the proper name for the mead hall where the men gather and celebrate in "Beowulf"?
The name of Hrothgar's mead hall is Heorot. Here is how it is described in the story:
I heard that orders to craft the gathering place were widely sent to many tribes throughout the earth. His plan achieved with swiftness, that hall, the greatest of buildings, stood there ready. He, whose words held dominion in many lands, gave it the name Heorot. Nor did he go back on his promise, but distributed rings and treasure at the banquet. The hall towered high, with pinnacles spanning the sky, as it awaited the scathing blasts of deadly flame. The day had not yet come when father and son-inlaw stood by with blade-baring hatred, stirred by a blood feud.
According to wikipedia, the word Heorot means "Hall of the Hart" (male deer).
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Hrothgar was successful in war, and had a great mead-hall built named Heorot (Heort), where he held court, doling out rings, neck chains, and other bounty. The celebrations and carousing in the new hall provoked envy in Grendel, a grim demon descended from Cain and condemned to be an outcast, living mysteriously in the nearby fen and heath. On his first attack, he hauled off 30 men to his lair, and gruesomely killed more the next night. The men took to sleeping in huts away from the hall, and for 12 years their king lived in humiliation as Grendel took over the hall and continued his ambushes. The plight of the kingdom became known far and wide.