The paper discusses the geometric Langlands program, focusing on its connection to quantum field theory, specifically $\mathcal{N} = 4$ super Yang-Mills theory in four dimensions. The authors describe how compactifying this theory on a Riemann surface leads to a family of topological field theories in two dimensions, with Hitchin's moduli space as the target. Key concepts include electric-magnetic duality, mirror symmetry, branes, Wilson and 't Hooft operators, and topological field theory. The paper explores how these concepts naturally arise from the physics, providing new insights into the geometric Langlands program, such as the appearance of Hecke eigensheaves and $\mathcal{D}$-modules. The authors also discuss the role of $S$-duality, the construction of topological field theories from $\mathcal{N} = 4$ super Yang-Mills, and the interpretation of certain operators and charges in the context of the geometric Langlands program.The paper discusses the geometric Langlands program, focusing on its connection to quantum field theory, specifically $\mathcal{N} = 4$ super Yang-Mills theory in four dimensions. The authors describe how compactifying this theory on a Riemann surface leads to a family of topological field theories in two dimensions, with Hitchin's moduli space as the target. Key concepts include electric-magnetic duality, mirror symmetry, branes, Wilson and 't Hooft operators, and topological field theory. The paper explores how these concepts naturally arise from the physics, providing new insights into the geometric Langlands program, such as the appearance of Hecke eigensheaves and $\mathcal{D}$-modules. The authors also discuss the role of $S$-duality, the construction of topological field theories from $\mathcal{N} = 4$ super Yang-Mills, and the interpretation of certain operators and charges in the context of the geometric Langlands program.