In Bredons "Topology and Geometry" [Chapter V, section 12] the following theorem is proven:
If $G$ is a compact connected Lie group its $k$-th cohomology $H^k(G,\mathbb{R})$ is isomorphic to the space of $k$-forms on the Lie algebra $\mathfrak{g}$ that are invariant under the action induced by $\mathrm{Ad} \colon G \to \mathrm{GL}(\mathfrak{g})$.
My question: Are there any interesting examples of Lie groups whose cohomology can be computed using this theorem apart from the $n$-torus $T^n= S^1 \times \ldots \times S^1$?
Thanks for your help!