[1] Since 2018, Lurie has been transferring the contents of Higher Topos Theory (along with new material) to Kerodon, an "online resource for homotopy-coherent mathematics"[2] inspired by the Stacks Project.
The first five of the book's seven chapters comprise a rigorous development of general ∞-category theory in the language of quasicategories, a special class of simplicial set which acts as a model for ∞-categories.
The path of this development largely parallels classical category theory, with the notable exception of the ∞-categorical Grothendieck construction; this correspondence, which Lurie refers to as "straightening and unstraightening",[3] gains considerable importance in his treatment.
Higher Topos Theory followed an earlier work by Lurie, On Infinity Topoi, uploaded to the arXiv in 2003.
"[1] Lurie released a draft of Higher Topos Theory on the arXiv in 2006,[5] and the book was finally published in 2009.