Answer
The first Habsburg King of Castile was Philip I, also known as Philip the Handsome, who ruled from 1504 until his death in 1506. He was the son of Maximilian I, Holy Roman Emperor, and Mary of Burgundy, and through his marriage to Joanna of Castile, he became King of Castile and Aragon, initiating the rule of the Habsburg dynasty in Spain, which would last for over two centuries.