  Real forms of a complex reductive group are classified by Galois cohomology
H^1(Gamma,G_ad) where G_ad is the adjoint group. Cartan's classification of
real forms in terms of maximal compact subgroups can be stated in terms of
H^(Z/2Z,G_ad) where the action is by a (holomorphic) Cartan involution. The
main result is that for any complex reductive group, possibly disconnected,
there is a canonical isomorphism between H^1(Gamma,G) and H^1(Z/2Z,G). As
applications we give short proofs of some well known results, including the
Sekiguchi correspondence, Matsuki duality, results on Cartan subgroups, the
rational Weyl group, and strong real forms. We also compute H^1(Gamma,G) for
all simple, simply connected real groups.
