UNIX and Linux don't incorporate the user interface into the kernel; instead, they let it be implemented by user level programs. This applies for both text mode and graphical environments.
This arrangement makes the system more flexible, but has the disadvantage that it is simple to implement a different user interface for each program, making the system harder to learn.
The graphical environment primarily used with Linux is called the X Window System (X for short). X also does not implement a user interface; it only implements a window system, i.e., tools with which a graphical user interface can be implemented. The three most popular user interface styles implemented over X are Athena, Motif, and Open Look.