The introduction to the book "Higher Topos Theory" by Jacob Lurie discusses the goal of understanding cohomology groups $\mathrm{H}^n(X; G)$ in more conceptual terms, particularly in the context of algebraic topology. It highlights the role of Eilenberg-MacLane spaces and $G$-torsors in this context. The text explains that $\mathrm{H}^1(X; G)$ can be understood through $G$-torsors, which are equivalent to continuous maps from $X$ to the classifying space $BG$. For higher cohomology groups, such as $\mathrm{H}^2(X; G)$, the concept of $G$-torsors is extended to $G$-stacks or gerbes. The book aims to develop a theory of $n$-stacks and $n$-topoi, which generalize the classical theory of Grothendieck toposes. The main goal is to provide an $\infty$-categorical version of topos theory, focusing on $(\infty, 1)$-categories. The book covers foundational concepts, fibrations of simplicial sets, limits and colimits, adjoint functors, and the theory of $\infty$-topoi, including their applications in homotopy theory and topology.The introduction to the book "Higher Topos Theory" by Jacob Lurie discusses the goal of understanding cohomology groups $\mathrm{H}^n(X; G)$ in more conceptual terms, particularly in the context of algebraic topology. It highlights the role of Eilenberg-MacLane spaces and $G$-torsors in this context. The text explains that $\mathrm{H}^1(X; G)$ can be understood through $G$-torsors, which are equivalent to continuous maps from $X$ to the classifying space $BG$. For higher cohomology groups, such as $\mathrm{H}^2(X; G)$, the concept of $G$-torsors is extended to $G$-stacks or gerbes. The book aims to develop a theory of $n$-stacks and $n$-topoi, which generalize the classical theory of Grothendieck toposes. The main goal is to provide an $\infty$-categorical version of topos theory, focusing on $(\infty, 1)$-categories. The book covers foundational concepts, fibrations of simplicial sets, limits and colimits, adjoint functors, and the theory of $\infty$-topoi, including their applications in homotopy theory and topology.