it's likely that you can use Game Maker also under Linux if you use wine. Accoding to this rating most versions should work ok on wine: http://appdb.winehq.org/objectManage...ation&iId=2965
Also there are many free Game engines (such as Panda3D, Irrlicht, Ogre3D, Cafu etc. etc.) which can be used on Linux. But the vast majority requires good programming language knowledge. If you want to learn a programming language I can recommend either python, because it's pretty easy and fast to program in python or C++, because it's commonly used in game engines. But C++ requires much more learning and patience. Programming in python is more fun. Free books to learn basic game making in python are here
(but of course to be a programmer this two books are not enough, you should know about object oriented programming as well for advanced games and engines).
I recently also read about Flare, where you probably wouldn't need programming knowledge: http://opengameart.org/forumtopic/ho...ame-with-flare