  These lectures are a pedagogical introduction to the application of
perturbative unitarity to Higgs physics within and beyond the Standard Model
(SM). I begin with a review of how perturbative unitarity arises from quantum
mechanical scattering theory and apply it to the classic problem of
longitudinal vector boson scattering in the SM to derive the famous upper bound
on the Higgs boson mass. I then consider extended Higgs sectors, using the
two-Higgs-doublet model, the scalar septet model, and the Georgi-Machacek model
as case studies. I discuss the resulting Higgs coupling sum rules as well as
the intertwined constraints on masses and couplings of the additional Higgs
bosons in these models, highlighting the connection between perturbative
unitarity and the decoupling limit. I finish with a direct review of the
decoupling limit in the two-Higgs-doublet model and a digression on the
alignment limit. These notes are based on lectures delivered over the past few
years in a graduate-level course on beyond-the-SM phenomenology and are meant
as a companion volume to my TASI 2013 lectures on Higgs physics.
