First, I'm a string theory student hoping to grasp some math involved in some physics developments.

I'm hoping to read the famous Kapustin-Witten Paper "Electric-magnetic duality and the geometric Langlands program" and the related "The Yang-Mills equations over Riemann surfaces".

The following statement serves to explain the origin of my trouble: Let $G$ be a simple complex Lie group and $C$ a Riemann surface. Geometric Langlands is a set of mathematical ideas relating the category of coherent sheaves over the moduli stack of flat $G^{L}$-bundles ($G^{L}$ is the dual Langlands group of $G$) over $C$ with the category of $\mathcal{D}$-modules on the moduli stack of holomorphic $G$-bundles over $C$.

**My problem:** I have working knowledge of representation theory, but I'm completely ignorant about the theory of mathematical stacks and the possible strategies to begin to learn it. What specifically worries me is how much previous knowledge of $2$-categories is needed to begin.

**My background:** I've read Hartshorne's book on algebraic geometry in great detail, specifically the chapters on varieties, schemes, sheaf cohomology and curves. My category theory and homological algebra knowledge is exactly that needed to read and solve the problems of the aforementioned book. I'm also familiar with the identification between the topological string $B$-model branes and sheaves at the level of Sharpe's lectures.

**My questions:** I'm asking for your kind help to find references to initiate me on the theory of stacks given my elementary background and orientation. I'm completely unfamiliar with the literature and the pedagogical routes to begin to learn about stacks.

Any suggestion will be extremely helpful to me.

**Update:** I have found the paper String Orbifolds and Quotient Stacks
very useful and explicit.

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