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Generalizing Tate's results for tori, we give closed formulas for the abelianGalois cohomology groups H^1_{ab}(F,G) and H^2_{ab}(F,G) of a connectedreductive group G over a global field F, and obtain formulas, suitable forcomputer calculatios, for the first nonabelian Galois cohomology set H^1(F,G)of G and for the second Galois cohomology group H^2(F,T) of an F-torus T.

Galois cohomology of reductive groups over global fields