for my little program I’d like to create a simple notification just like this(for example):

I do not know where to start, Any helps ?
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Do you want something in the taskbar (next to the clock) or something that pops up an animation like that too?
There is a brief (but good place to start) doc here for the system tray:
http://java.sun.com/developer/technicalArticles/J2SE/Desktop/javase6/systemtray/
Also have a look into the Swing timers, they can help you create animations:
http://docs.oracle.com/javase/tutorial/uiswing/misc/timer.html