Bredon cohomology is a cohomology theory that applies to topological spaces equipped with the group actions. The thesis is directed towards computation of rational Bredon cohomology of equivariant polyhedral products and equivariant configuration spaces in the case when the acting groups are small non-abelian groups.

A polyhedral product is a natural subspace of a Cartesian product, which is specified by a simplicial complex $K$. The automorphism group Aut(K) of K induces a group action on the polyhedral product. In the thesis we study this group action and give a formula for the fixed point set of the polyhedral product for any subgroup H of Aut(K). We use the fixed point data to compute examples of Bredon cohomology.

A configuration space of a topological space X refers to the topological space of pairwise distinct points in X. For any group G, given a real linear representation V, the configuration space of V has a natural diagonal G-action. In the thesis we study this group action on the configuration space and give a decomposition of the homology Bredon coefficient system of the configuration space and apply this to compute Bredon cohomology of the configuration space.