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Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.
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Cohomology rings of $ GL_n(C)$, $SL_n(C)$
For classical groups such as $GL_n(F)$, $SL_n(F)$ for $F = \mathbb{R}, \mathbb{C}$,
$SU(n)$, $U(n)$ and $O(n)$, you may find the cohomology ring structure and its proof in M. Mimura and H. Toda, Topo …