  Real forms of a complex reductive group are classified in terms of Galois
cohomology $H^1(\Gamma,G_{ad})$ where $G_{ad}$ is the adjoint group.
Alternatively, the theory of the Cartan involution gives a description in terms
of cohomology with respect to a holomorphic involution: $H^1(\mathbb Z/2\mathbb
Z,G_{ad})$ where the non trivial element acts by a holomorphic involution
$\theta$.
  The main theorem is that in general, if $\theta$ is the Cartan involution of
a real form $\sigma$, there is a canonical isomorphism $H^1(\Gamma,G)\simeq
H^1(\mathbb Z/2\mathbb Z,G)$.
  This has applications to the structure and representation theory of real
groups. We give two such applications. The first is a simple proof of Matsuki's
result on conjugacy classes of tori in real groups. The second is a computation
of $H^1(\Gamma,G)$ in general. The answer is expressed in terms of the notion
of strong real forms. We include tables for all simply connected simple groups.
