  These notes form the second part of a detailed account of the theory of
nilspaces developed by Camarena and Szegedy. Here we focus on nilspaces
equipped with a compact topology that is compatible with the cube structure,
called compact nilspaces. The material in these notes relies on the first part
of our exposition (available as arXiv:1601.03693), and it expands on the third
chapter of the paper of Camarena and Szegedy, providing more detailed proofs of
their results. To that end we also include several additional results that are
implicit in their paper.
