\begin{equation*} \DeclareMathOperator\Coim{Coim} \DeclareMathOperator\Coker{Coker} \DeclareMathOperator\Ext{Ext} \DeclareMathOperator\Hom{Hom} \DeclareMathOperator\Im{Im} \DeclareMathOperator\Ker{Ker} \DeclareMathOperator\Mor{Mor} \DeclareMathOperator\Ob{Ob} \DeclareMathOperator\Sh{Sh} \DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}} \DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}} \DeclareMathOperator\Spec{Spec} \newcommand\colim{\mathop{\mathrm{colim}}\nolimits} \newcommand\lim{\mathop{\mathrm{lim}}\nolimits} \newcommand\Qcoh{\mathit{Qcoh}} \newcommand\Sch{\mathit{Sch}} \newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}} \newcommand\Cohstack{\mathcal{C}\!\mathit{oh}} \newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}} \newcommand\Quotfunctor{\mathrm{Quot}} \newcommand\Hilbfunctor{\mathrm{Hilb}} \newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}} \newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}} \newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}} \newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits} \newcommand\Picardstack{\mathcal{P}\!\mathit{ic}} \newcommand\Picardfunctor{\mathrm{Pic}} \newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}} \end{equation*}

The Stacks project

  • Vistoli: Notes on Grothendieck topologies, fibered categories and descent theory [vistoli_fga]

    Contains useful facts on fibered categories, stacks and descent theory in the fpqc topology as well as rigorous proofs.
  • Knutson: Algebraic Spaces [Kn]

    This book, which evolved from his PhD thesis under Michael Artin, contains the foundations of the theory of algebraic spaces. The book [LM-B] frequently references this text. See also Artin's papers on algebraic spaces: [Artin-Algebraic-Approximation], [ArtinI], [Artin-Implicit-Function], [ArtinII], [Artin-Construction-Techniques], [Artin-Algebraic-Spaces], [Artin-Theorem-Representability], and [ArtinVersal]
  • Grothendieck et al, Théorie des Topos et Cohomologie Étale des Schémas I, II, III also known as SGA4 [SGA4]

    Volume 1 contains many general facts on universes, sites and fibered categories. The word “champ” (French for “stack”) appears in Deligne's Exposé XVIII.
  • Jean Giraud: Cohomologie non abélienne [giraud]

    The book discusses fibered categories, stacks, torsors and gerbes over general sites but does not discuss algebraic stacks. For instance, if $G$ is a sheaf of abelian groups on $X$, then in the same way $H^1(X, G)$ can be identified with $G$-torsors, $H^2(X, G)$ can be identified with an appropriately defined set of $G$-gerbes. When $G$ is not abelian, then $H^2(X, G)$ is defined as the set of $G$-gerbes.
  • Kelly and Street: Review of the elements of 2-categories [kelly-street]

    The category of stacks form a 2-category although a simple type of 2-category where are 2-morphisms are invertible. This is a reference on general 2-categories. I have never used this so I cannot say how useful it is. Also note that [stacks-project] contains some basics on 2-categories.

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