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A Graphical User Interface or GUI (as opposed to a text based interface) introduces concepts such as windows, icons, menus and pointers (WIMP) in an attempt to give the user a more intuitive and productive working environment. The basis of most graphical software on Linux and other Unix systems is the X Window System, under its most common guise of XFree86.
This is supplemented by a window manager and often some sort of GUI toolkit, such as Qt or GTK, is used by programmers to construct an application.