The group action on a topological space describes its symmetry property. Equivariant cohomology theories are major tools that help us to understand the topology information of those group action. Moreover, they connect the group representation and group cohomology with the group action and cohomology of a space. In this oral exam, we are going to talk about the basic setting of Bredon coefficient system, define Bredon cohomology and polyhetra product, and explore some possible computations.