  Eight Majorana fermions in $d=1+1$ dimensions enjoy a triality that permutes
the representation of the $SO(8)$ global symmetry in which the fermions
transform. This triality plays an important role in the quantization of the
superstring, and in the analysis of interacting topological insulators and the
associated phenomenon of symmetric mass generation. The purpose of these notes
is to provide an introduction to the triality and its applications, with
careful attention paid to various ${\bf Z}_2$ global and gauge symmetries and
their coupling to background spin structures.
