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Using a reduction of the Galois cohomology of a linear algebraic group $G$ tothat of a certain finite subquotient, we give different formulas allowing thecalculation of the unramified algebraic Brauer group of a homogeneous space$V=G\backslash G'$ with $G'$ semisimple and simply connected, both over afinite field and over an arbitrary field of characteristic $0$.

Groupe de Brauer non ramifi\'e alg\'ebrique des espaces homog\`enes (The unramified algebraic Brauer group of homogeneous spaces)