Nightmare is a fictional character, a supernatural being who has appeared in many Marvel Comics stories, most commonly as one of Doctor Strange and Ghost Rider's major enemies.
The character was created by Stan Lee and Steve Ditko in Strange Tales #110 (July 1963), the very same issue where the Master of the Mystic Arts first appeared.
He is the evil ruler of a 'dream dimension', where tormented humans are brought during their sleep. He roams this realm on his demonic black horned horse named Dreamstalker. He appears as a chalk-white man with wild green hair, a green bodysuit, and a ragged cape.
Nightmare is a demon from the dimension Everinnye, like his "cousin", the Dweller-in-Darkness. Nightmare is dependent on the human race's need to dream. Without this ability, Nightmare would cease to exist, but humanity would go insane. At one point Strange and Nightmare had to join forces to prevent that from happening. Nightmare has run afoul of Spider-Man, Captain America, Ghost Rider, Dazzler, Wolverine, and the Hulk on different occasions. Nightmare also served under Shuma-Gorath and warned Strange that the demon would be a force that even the Sorcerer Supreme would have trouble defeating, and he once joined the Fear Lords, a group of supernatural creatures who fed on fear, to attack Dr. Strange together. Their plans were undone when D'spayre tricks him into competing with the Dweller-in-Darkness over who could frighten humanity more.
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Links: Nightmare's Wiki entry Algebra.com entry Official Marvel entry