I'm typing lecture notes for my course held at the QED Academy 2023. The goal of that course was twofold: To introduce ∞-category theory, but also to show how this abstract formalism can be used to do actual topology. I can't say how much I succeeded in that, but at least I managed to have the Adams spectral sequence on the board in the end 😎💪.
These notes give me the chance to add many technical details that inevitably had to be omitted in the course. I also hope they will come in handy if I decide to hold a course like that again ♻️.
📋 A compiled PDF can be found here.