Super Mario Galaxy is the first installment of the Super Mario Galaxy series and the first 3D Game for the Wii. It is based on Super Mario 64 and Super Mario Sunshine, two games that had 3D.
Peach has invited Mario to the Star Festival in Toad Town (known as Caste Gardens which would where the last power star and galaxy reside). When Mario arrives at Peach's Castle, Bowser and Bowser, Jr. arrive in Castle Gardens in their airship. Peach is on the balcony holding a Luma. Bowser plans to create a whole new galaxy with Peach's help, but Peach doesn't respond. Mario attempt to reach Peach but Kamek knocks him out of the World. Bowser then sends Peach's Castle upwards for his new galaxy.
Mario wakes up at the Gate. Mario meets a Luma who gives the Spin Attack power. He then finds out he was saved by Rosalina. Rosalina brings him to the Comet Observatory and shows him Bowser attacked the Observatory and stole all the Grand and Regular Power Stars needing Mario's help. Mario then travels in all the domes to collect power stars so they can travel to the Center of the Universe to defeat Bowser.
When they reach Bowser and Bowser, Jr., Bowser tells Mario that his galaxy is almost completed with Peach's help. Bowser than battles Mario on three planets. On the final planet, Mario knocks Bowser into the star. Mario obtains the Grand Star and flies with Peach to the Mushroom Kingdom. As Bowser's galaxy dies, a black hole occurs and they are all sucked in. They later wake up in the Star Festival with everyone happy after Rosalina appears in front of Mario and tells the story of the Lumas.
After collecting all the regular Power Stars. They confront Bowser again who has kidnapped Peach again. After he is defeated, Super Luigi Galaxy can be played. After 120 Power Stars are collected for each character, each character can play the mission: The Star Festival in galaxy, Grand Finale Galaxy (it is located at Castle Gardens). After it is beaten for each character, the character will recieve a note on the Wii Message Board by Mailtoad.
In Super Mario Galaxy, some Worlds are known as Domes with each Dome giving access to a few galaxies.