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Teach Marshall D. (マーシャル・D・ティーチ)Blackbeard was formerly a member of the Whitebeard Pirates second division led by Portgas D. Ace. Shanks also warned Whitebeard that Blackbeard was becoming stronger than him and had only joined his crew to stay hidden behind the massive shadow of the Whitebeard name, until he became strong enough to make his move. This time came when Blackbeard murdered a member of the Whitebeard Pirates, thus prompting his departure from the crew, and Ace's hunt for him. Blackbeard was also the one who gave Shanks the scars around his eye, a long time ago. Shanks also tells Whitebeard to call back Ace on his hunt for Blackbeard, as he was concerned about the timing of a confrontation between Ace and Blackbeard.
After Luffy defeated Crocodile in Alabasta, Lafitte tried to nominate Blackbeard to become one of the Shichibukai to take Crocodile's place, but in order to be accepted, Blackbeard must first build up a fearsome reputation.
Blackbeard happened to be in Jaya, at the same time Luffy was. Both Luffy and Blackbeard seem to strike up a rivalry when they nearly got into a fight over how they like or dislike one of the island tavern's food. However, not long after that he'd given Luffy a friendly speech about how pirates will never stop dreaming. Despite their similarities (and comical contrasts), it was revealed in the Jaya arc that Blackbeard was looking to take out a strong pirate to make a name for himself - and he chose Luffy after learning of his 100 million Belli bounty at the time. He however failed to catch them as they were blasted aside by the knock-up stream which took the Straw Hats to Skypiea.
(Source: One Piece Wikia)