Familiarizing with the Grothendieck topos $\mathbf{B}G$. I am trying to familiarize with the Grothendieck topos $\mathbf{B}G$ of continuous $G$-sets, where $G$ is a topological group. 
I am unfortunately not very familiar with working with different topologies on groups; I am asking for a reference that covers topological group actions at a fairly elementary level - at a level that will allow me to understand the basic constructions needed in the topos. It would be ideal if the reference has a category-theory flavor. Thanks for any help!

Mac Lane's and Moerdijk's Sheaves in Geometry and Logic contains a section about that topos (III.9). It seems accessible without extended knowledge about continuous group actions.
