(This is a presentation I gave for Bill Weiss’ course Set-Theoretic Topology on April 19, 2013. In class we discussed some cardinal invariants and how they are related; here I will survey what happens when we look at the cardinal invariants of topological groups.)
This review follows very closely the discussion in section 5.2 of Arhangel’skii and Tkachenko’s book “Topological Groups and Related Structures“. Another good resource is section 3 of Comfort’s article “Topological Groups” in the Handbook of Set-Theoretic Topology. The only thing I claim to be my own are the (unsourced) pictures I have provided.