Infinity category theory from scratch (4 lectures)
Emily Riehl - Young Topologists Meeting Lecture, 2019.
An introduction to homotopical categories (4 lectures)
Julie Bergner - MSRI Summer School at CIMAT, 2014.
Introduction to infinity category theory
David Gepner - IWoAT Summer School on Chromatic Homotopy Theory and Higher (Infinity-Categorical) Algebra, 2022.
Category Theory
Part III course by Tom Leinster in 2000 at the University of Cambridge. The problem sets are especially useful!
Introduction to quasicategories
Charles Rezk, course notes.
Category theory in context
Emily Riehl, 2014.
Basic Category Theory
Tom Leinster, 2014.
Model Categories
Mark Hovey, 1999.
Categories for the Working Mathematician
Saunders Mac Lane, 1978.
Homotopical categories: from model categories to (∞,1)-categories
Emily Riehl, 2019.
The homotopy theory of (∞,1)-categories
Julie Bergner, 2018
Higher Topos Theory
Jacob Lurie, 2012.
Higher Algebra
Jacob Lurie, 2017.
Introduction to Infinity Categories (textbook)
Markus Land, 2021.