Higher Topos Theory

Higher Topos Theory is a mathematical book by American mathematician Jacob Lurie. The main subject of the book is an ∞-topos. But it also develops the theory of ∞-category as a particular kind of a simplicial set. All together the book provides a categorical foundation for derived algebraic geometry.

The book is available at arXiv:math/0608040, although the copy hosted on Lurie's website has been updated more recently. Since 2018 Lurie has been porting the content of HTT over to a Stacks Project-like web platform, Kerodon, and adding new material.