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There are many hidden stars throughout the game, almost one in each galaxy. The appear once you've completed all the normal levels in the galaxy. They're shown by a ? above a level, or a ? Star when you're moused over a galaxy. To see how to get these stars, go to the galaxy name in the menu, and the walkthrough is there.
Also, there are three green stars hidden throughout the game. There is no indication that these stars are hidden, you must find them on your own. Walkthroughs are in the Green Stars and Trial Galaxies page. Once you've collected all of them, three green Lumas become a Launch Star in the Observatory which will launch you to a small planet. Here, you have access to the three Trial Galaxies, each with only one star.