I hope to know the classification of real forms of complex simple Lie algebras of types A, D, E $A$, $D$, $E$ up to inner automorphisms.
Let g_1 $\mathfrak{g}_1$ and g_2 $\mathfrak{g}_2$ be real forms of a complex simple Lie algebra g. $\mathfrak{g}$. We say that they are equivalent if there is an isomorphism g_1 ---> g_2 $\mathfrak{g}_1 \to \mathfrak{g}_2$ which extends to an inner automorphism of g. This $\mathfrak{g}$. However, there may result in be real forms which are isomorphic but not equivalent.
Where can we find the classification of such equivalence classes of real forms?
