The book *Large Networks and Graph Limits* by László Lovász is a comprehensive treatise on the theory of graph limits, aimed at graduate students and research mathematicians interested in graph theory and its applications to large networks. The book is divided into five parts, with the first part providing an introduction and the last part offering a glimpse into potential extensions to other combinatorial structures. The central parts delve into graph algebras, limits for sequences of dense graphs, and limits for sequences of bounded degree graphs. The book begins with an informal introduction to large networks, covering key concepts such as sampling, partitioning, homomorphisms, and graph distances. It then explores the algebra of graph homomorphisms, introducing graph parameters, connection matrices, and the concept of graph algebras. The third part focuses on the analysis of dense graph sequences, defining limit objects called graphons and developing the theory of graphon spaces, including cut norms, cut distances, and regularity lemmas. The fourth part discusses the convergence of dense graph sequences, showing how graphons can be used to capture the limits of such sequences. It covers various methods for establishing convergence and determining the limit graphon, including the use of random graph models and ultralimits. The final part explores the structure of graphons and their applications, highlighting their role in simplifying reasoning about large graph sequences. The book is rich in detail, with 23 chapters, an appendix, and a comprehensive bibliography. It includes numerous exercises to reinforce understanding and encourages readers to explore the area further. Lovász's writing is both insightful and accessible, making it a valuable resource for those interested in the前沿 of graph theory and its applications.The book *Large Networks and Graph Limits* by László Lovász is a comprehensive treatise on the theory of graph limits, aimed at graduate students and research mathematicians interested in graph theory and its applications to large networks. The book is divided into five parts, with the first part providing an introduction and the last part offering a glimpse into potential extensions to other combinatorial structures. The central parts delve into graph algebras, limits for sequences of dense graphs, and limits for sequences of bounded degree graphs. The book begins with an informal introduction to large networks, covering key concepts such as sampling, partitioning, homomorphisms, and graph distances. It then explores the algebra of graph homomorphisms, introducing graph parameters, connection matrices, and the concept of graph algebras. The third part focuses on the analysis of dense graph sequences, defining limit objects called graphons and developing the theory of graphon spaces, including cut norms, cut distances, and regularity lemmas. The fourth part discusses the convergence of dense graph sequences, showing how graphons can be used to capture the limits of such sequences. It covers various methods for establishing convergence and determining the limit graphon, including the use of random graph models and ultralimits. The final part explores the structure of graphons and their applications, highlighting their role in simplifying reasoning about large graph sequences. The book is rich in detail, with 23 chapters, an appendix, and a comprehensive bibliography. It includes numerous exercises to reinforce understanding and encourages readers to explore the area further. Lovász's writing is both insightful and accessible, making it a valuable resource for those interested in the前沿 of graph theory and its applications.