A thin film transistor with excellent electric characteristics, a display device having the thin film transistor, and a method for manufacturing the thin film transistor and the display device in a high yield are provided. In the thin film transistor, a gate electrode, a gate insulating film, crystal grains that mainly contain silicon and are provided for a surface of the gate insulating film, a semiconductor film that mainly contains germanium and covers the crystal grains and the gate insulating film, and a buffer layer in contact with the semiconductor film that mainly contains germanium overlap with one another. Further, the display device has the thin film transistor.