The paper by Ginzburg and Kapranov aims to connect two seemingly disparate areas: Kontsevich's graph cohomology and the theory of Koszul duality for quadratic associative algebras. The main unifying concept is that of an operad. The first part of the paper establishes a relationship between operads, moduli spaces of stable curves, and graph complexes. Each operad is associated with a collection of sheaves on moduli spaces, and the cobar complex of an operad is shown to be equivalent to a graph complex. This construction is interpreted as a special case of Verdier duality for sheaves. The second part introduces quadratic operads and a distinguished subclass called Koszul operads. The authors define a natural duality on quadratic operads, which is analogous to the duality of Priddy for quadratic associative algebras. This duality is shown to be closely related to the cobar construction and graph complexes. The paper also discusses the relevance of operads to conformal field theory and the combinatorics of moduli spaces of stable curves. The authors provide a detailed introduction to trees, $k$-linear operads, algebraic operads, and geometric operads. They define operads in monoidal categories and discuss examples such as associative, commutative, and Lie algebras. The paper concludes with a discussion of the configuration operad and its stratification, and the construction of combinatorial sheaves on moduli spaces.The paper by Ginzburg and Kapranov aims to connect two seemingly disparate areas: Kontsevich's graph cohomology and the theory of Koszul duality for quadratic associative algebras. The main unifying concept is that of an operad. The first part of the paper establishes a relationship between operads, moduli spaces of stable curves, and graph complexes. Each operad is associated with a collection of sheaves on moduli spaces, and the cobar complex of an operad is shown to be equivalent to a graph complex. This construction is interpreted as a special case of Verdier duality for sheaves. The second part introduces quadratic operads and a distinguished subclass called Koszul operads. The authors define a natural duality on quadratic operads, which is analogous to the duality of Priddy for quadratic associative algebras. This duality is shown to be closely related to the cobar construction and graph complexes. The paper also discusses the relevance of operads to conformal field theory and the combinatorics of moduli spaces of stable curves. The authors provide a detailed introduction to trees, $k$-linear operads, algebraic operads, and geometric operads. They define operads in monoidal categories and discuss examples such as associative, commutative, and Lie algebras. The paper concludes with a discussion of the configuration operad and its stratification, and the construction of combinatorial sheaves on moduli spaces.