TITLE: lists of computed cohomologies?
QUESTION [7 upvotes]: Is there any comprehensive list of examples for computed
1) de-Rham cohomology-groups
2) Lie-algebra-cohomology groups $H^i(\mathfrak{g},\mathbb{R})$
3) equivariant de-Rham cohomology groups ?
Especially I am interested in a comprehensive list of examples (or classes of examples) of
a) manifolds with vanishing first and second de-Rham-cohomology
b) lie-algebras with vanishing first and second lie-algebra-cohomology

REPLY [11 votes]: Chevalley and Borel calculated the cohomology of many Lie groups and Landweber collected those results here in just two pages: it describes the cohomology of $U(n)$, $SU(n)$, $SO(n)$, $G_2$, $F_4$, $E_6$, $E_7$ and $E_8$. 
You might also enjoy Neil Strickland's bestiary of topological spaces and spectra, which lists the (co)homology of many topological spaces.