From the Super Mario Wiki
The Crystal Stars are the seven stars Mario, Goombella, Koops, Flurrie, Yoshi, Vivian, Admiral Bobbery and possibly Ms. Mowz collect in Paper Mario: The Thousand-Year Door. They open the Thousand-Year Door to the Palace of Shadow and will teach Mario seven special moves. They consist of the Diamond Star, the Emerald Star, the Gold Star, the Ruby Star, the Sapphire Star, the Garnet Star and the Crystal Star.
The stars were created by the Shadow Queen to hold the essence of the heavens, but the four heroes collected them and used their power against the Queen. One of the castles built to hold the stars is Hooktail Castle.
Hooktail has the Diamond Star, the Puni Elder has the Emerald Star (Mario had to defeat Magnus Von Grapple to get it), Grubba has the Gold Star, Doopliss has the Ruby Star, Cortez has the Sapphire Star, Pennington has the Garnet Star in his home, and Magnus Von Grapple 2.0 (Lord Crump) has the Crystal Star.
The Crystal Star' Powers
Names in other languages