One can think of Lurie’s book as a comprehensive study of the generalization of the above statement from $1$ to $(\infty,1)$ (recall the notion of (n,r)-category):
Based on work by André Joyal on the quasi-category model for (∞,1)-categories, Lurie presents a comprehensive account of the theory of (∞,1)-categories including the definitions and properties of all the standard items familiar from category theory (limits, fibrations, etc.)
Second part, sections 5-7
Given the $(\infty,1)$-categorical machinery from the first part there are natural $(\infty,1)$-categorical versions of $(\infty,1)$-presheaf and $(\infty,1)$-sheaf categories (i.e. $(\infty,1)$-categories of ∞-stacks): the “$\infty$-topoi” that give the book its title (more descriptively, these would be called “Grothendieck $(\infty,1)$-topoi”). Lurie investigates their properties in great detail and thereby in particular puts the work by Brown, Joyal, Jardine, Toën on the model structure on simplicial presheaves into a coherent $(\infty,1)$-categorical context by showing that, indeed, these are models for ∞-stack (∞,1)-toposes.
How to read the book
1-categorical background
The book Higher topos theory together with Lurie’s work on Stable ∞-Categories is close to an $(\infty,1)$-categorical analog of the 1-categorical material as presented for instance in
The book discusses crucial concepts and works out plenty of detailed properties. On first reading it may be helpful to skip over all the technical parts and pick out just the central conceptual ideas. These are the following: