Lecture Notes on Modular Infinity Operads and Grothendieck-Teichmueller Theory

These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the “Higher Structures and Operadic Calculus” workshop. The goal of the series was to introduce and motivate modular infinity operads via their application to what is often called “Grothendieck-Teichmueller” theory.