  Control and manipulation of electromagnetic waves has reached a new level
with the recent understanding of topological states of matter. These
metamaterials have the potential to revolutionize many areas in traditional
electromagnetic design, from highly robust cavities to small footprint
waveguides. Much of the past literature has been on the cutting edge of
condensed matter physics, but there is now ample opportunity to explore their
usage for practical microwave and optical devices. To assist the beginner, in
this Tutorial we give a basic introduction to the essential concepts of
topological phenomena in electromagnetic systems, including geometric phases,
topological invariants, pseudospin states, and the integer/valley/spin quantum
Hall effects. Our focus is on engineered photonic topological insulators (PTIs)
in two-dimensional systems. We highlight methods for characterizing such
structures and how they result in unique wave-guiding properties. In addition,
we provide recipes on how to realize PTIs using photonic crystals and
metasurfaces, examine differences between different types of PTIs, and discuss
limitations and advantages of some of the existing enabling platforms.
