Let $G$ be a topological group. We give the existence of an equivariant homology and cohomology theory, defined on the category of all $G$-pairs and $G$-maps, which both satisfy all seven equivariant Eilenberg-Steenrod axioms and have a given covariant and contravariant, respectively, coefficient system as coefficients.In the case that $G$ is a compact Lie group we also define equivariant $CW$-complexes and mention some of their basic properties.The paper is a short abstract and contains no proofs.

Complexes of groups $G\left(X\right)$ over ordered simplicial complexes $X$ are generalizations to higher dimensions of graphs of groups. We first relate them to complexes of spaces by considering their classifying space $BG\left(X\right)$. Then we develop their homological algebra aspects. We define the notions of homology and cohomology of a complex of groups $G\left(X\right)$ with coefficients in a $G\left(X\right)$-module and show the existence of free resolutions. We apply those notions to study extensions of complexes of groups with constant or abelian kernel....