what is the plot behind this game?
Princess Peach discovers a star shaped creature called a Luma and invites Mario to come to the festival to see the Luma she discovered. Just as Mario gets there, Bowser invades the Mushroom Kingdom in a fleet of airships.
Super Mario Galaxy
The centennial Star Festival is held every hundred years to watch a comet in the Mushroom Kingdom. Princess Peach discovers a star shaped creature called a Luma and invites Mario to come to the festival to see the Luma she discovered. Just as Mario gets there, Bowser invades the Mushroom Kingdom in a fleet of airships. He invites Peach to his creation of his galaxy and removes Peach's castle from its foundations using a giant flying saucer and lifts it into outer space. 
what is super mario galaxy? 2007 platform action-adventure video game
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Super Mario Galaxy [SEP] Plot
The centennial Star Festival is held every hundred years to watch a comet in the Mushroom Kingdom. Princess Peach discovers a star shaped creature called a Luma and invites Mario to come to the festival to see the Luma she discovered. Just as Mario gets there, Bowser invades the Mushroom Kingdom in a fleet of airships. He invites Peach to his creation of his galaxy and removes Peach's castle from its foundations using a giant flying saucer and lifts it into outer space. Kamek, one of Bowser's minions, launches Mario, who tried to rescue Princess Peach, into space and onto a small planet with his magic while the Luma escapes from her hands.