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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.
External links

http://ncatlab.org/nlab/show/Higher+Topos+Theory
If I want to study Jacob Lurie's books “Higher Topoi Theory”, “Derived AG”, what prerequisites should I have?
http://www.math.harvard.edu/~lurie/
https://kerodon.net/about

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