Prince Rhaegar Targaryen was the eldest son and heir to King Aerys II Targaryen, Prince of Dragonstone. He was the older brother of Viserys and Daenerys Targaryen and the husband of Elia Martell, with whom he had two children: Rhaenys and Aegon Targaryen.

Secretly, however, Rhaegar annulled his marriage with Elia and married Lyanna Stark. Rhaegar's alleged "abduction" of Lyanna sparked Robert's Rebellion, as Lyanna was betrothed to Robert Baratheon. Robert killed Rhaegar at the climactic Battle of the Trident, and then deposed the Targaryen dynasty. Lyanna's brother Eddard Stark found her soon afterwards, as she was dying from childbirth. She was giving birth to her son with Rhaegar. To protect the child from Robert and others who sought the destruction of House Targaryen, Eddard passed him off as his bastard son that he fathered during the war: Jon Snow.

(source GOT wiki)

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