  Four lectures on invertible field theories at the Park City Mathematics
Institute 2019. Cobordism categories are introduced both as plain categories
and topologically enriched. We then discuss localization of categories and its
relationship to classifying spaces, and state the main theorem of
classification of invertible field theories in these terms. We also discuss
symmetric monoidal structures and their relationship to actions of the little
disk operads. In the final lecture we discuss an application of cobordism
categories to characteristic classes of surface bundles. Emphasis will be on
self-contained definitions and statements, referring to original literature for
proofs. We also include problem sets from the three exercise sessions at the
summer school, and solutions to two problems.
