  We provide a pedagogical technical guide to many of the key theoretical tools
and ideas that underlie work in the field of Floquet engineering. We hope that
this document will serve as a useful resource for new researchers aiming to
enter the field, as well as experienced researchers who wish to gain new
insight into familiar or possibly unfamiliar methods. This guide was developed
out of supplementary material as a companion to our recent review, "Band
structure engineering and non-equilibrium dynamics in Floquet topological
insulators," Nature Reviews Physics 2, 229 (2020). The primary focus is on
analytical techniques relevant for Floquet-Bloch band engineering and related
many-body dynamics. We will continue to update this document over time to
include additional content, and welcome suggestions for further topics to
consider.
