  After briefly recalling the quantum entanglement-based view of topological
phases of matter in order to outline the general context, we give an overview
of different approaches to the classification problem of topological insulators
and superconductors of non-interacting Fermions. In particular, we review in
some detail general symmetry aspects of the "ten-fold way" which forms the
foundation of the classification, and put different approaches to the
classification in relationship with each other. We end by briefly mentioning
some of the results obtained on the effect of interactions, mainly in three
spatial dimensions.
