  We present a proof of Thue-Siegel-Roth's Theorem (and its more recent
variants, such as those of Lang for number fields and that "with moving
targets" of Vojta) as an application of Geometric Invariant Theory (GIT).
Roth's Theorem is deduced from a general formula comparing the height of a
semi-stable point and the height of its projection on the GIT quotient. In this
setting, the role of the zero estimates appearing in the classical proof is
played by the geometric semi-stability of the point to which we apply the
formula.
