Cohomological Invariants for G-Galois Algebras and Self-Dual Normal Bases. We define degree two cohomological invariants for $G$-Galois algebras over fields of characteristic not 2, and use them to give necessary conditions for the existence of a self--dual normal basis. In some cases (for instance, when the field has cohomological dimension $\le 2$) we show that these conditions are also sufficient.