∞-categories: a first course
The language of ∞-categories has permeated a large body of modern mathematics, particularly in algebraic geometry and algebraic topology. (Just as the language of ordinary categories has done before that.) This course will teach you the very basics of this language. I will assume familiarity with ordinary category theory (some algebraic topology would be useful for intuition but it isn't necessary) and by the end you should be able to read research articles written in the language of ∞-categories, and to tackle more advanced texts developing the theory, such as the books of Lurie, Cisinski or Land.
This is an introduction to (singular) homology, following Hatcher's book. See the links below for details.
Updated lecture notes will be available on the Moddle page.
Once they're stable, I will also post them here.