Luke
Luke was one of the first vampires that Buffy faced upon moving to Sunnydale. He summoned The Master up from a pool of water deep within the bowels of the earth. Because he was then the strongest of The Master's brood, he was chosen to become "The Vessel" -- each life he took would imbue The Master with enough power to break free of and open the Hellmouth.
Buffy first meets Luke in the mausoleum and manages to escape from him. The next night, Luke leads the other vampires to the Bronze to accomplish said task of empowering The Master.
It is here that Buffy triumphs over Luke. He was slayed Buffy at the Bronze before he could free The Master
Jesse
Debut -- Welcome to the Hellmouth (Season 1)
Died -- The Harvest (Season 1)
Jesse is introduced as Xander's other best friend. He's got a sense of humor, but is not too smooth with the ladies. Jesse has a thing for Cordelia, and she's constantly insulting him, walking away from him, turning him down. Jesse meets Darla at the Bronze and leaves with her. When we next see Jesse at the mausoleum, he's already been bitten.
Buffy fights off the vampires and then goes to find Willow, Xander, and Jesse, who've left the mausoleum but are still being hunted by the vamps. We learn that Jesse got dragged off by a vampire.
In The Master's lair, Jesse's fate is decided -- he's to be bait to lure the Slayer down to the lair. And the next day, Xander and Buffy go down to look for Jesse. When they see him, they're relieved, but it soon becomes apparent that Jesse's now a vampire!
That night at The Bronze, when the vamps go hunting for The Master, we see Jesse wearing his normal face while he dances with Cordelia. Then he goes vampy. Xander's been told by Giles that Jesse is no longer Jesse, but is in fact a demon wearing Jesse's face and retaining Jesse's memories.
Jesse tells Xander "I'm a new man!" and is ready to kill Xander. Xander's holding a stake out to fend Jesse off, and in the panic to get out of the Bronze, someone runs by and bumps into Jesse, causing him to impale himself on Xander's stake.
Jesse is the first friend Xander loses to vampiric activity.
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