When I press on the Play button and when I am in the menu of the game (with buttons like Singleplayer, Multiplayer etc.) and then I press F11, Minecraft gets bigger but I can see through it. I can't see the game, I can only see my desktop through Minecraft. Thanks!
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This is still a thing, fullscreen doesn't work at all on Fedora 20.1 or Ubuntu 13.10. It works fine on Xubuntu 12.04 and the latest CrunchBang.
Take a look at the comments in MC-2067. This issue may be a duplicate of that one, and the information there may help you resolve the problem.