The book "Locally Convex Spaces" by Dr. phil. Hans Jarchow, published by B. G. Teubner in 1981, is a comprehensive treatise on locally convex spaces. The author, a professor at the University of Zürich, has drawn from his extensive teaching experience at both the University of Zürich and the University of Maryland over seven years. The book is designed for students with a background in general topology and basic measure theory, but it also includes advanced topics that may appeal to more specialized readers. The content is divided into three parts: Part I covers the elementary theory of general topological vector spaces, including linear spaces, topological vector spaces, completeness, and inductive linear topologies. Part II delves into the duality theory for locally convex spaces, discussing dual pairings, weak topologies, continuous convergence, and related topics. Part III focuses on tensor products and nucularity, exploring projective and injective tensor products, classes of operators, and the approximation property. Key topics include the Hahn-Banach theorem, the Krein-Milman theorem, the Riesz representation theorem, barrelled spaces, reflexive spaces, and nuclear spaces. The book also introduces new perspectives on certain well-known concepts, such as local convergence and Schwartz spaces, and provides a detailed treatment of bornological and ultrabornological spaces. The preface outlines the book's structure, references, and the author's intentions, emphasizing the book's systematic approach and its contributions to the field. The author acknowledges the valuable suggestions and support received from colleagues and publishers, and expresses gratitude to his family for their encouragement and assistance during the writing process.The book "Locally Convex Spaces" by Dr. phil. Hans Jarchow, published by B. G. Teubner in 1981, is a comprehensive treatise on locally convex spaces. The author, a professor at the University of Zürich, has drawn from his extensive teaching experience at both the University of Zürich and the University of Maryland over seven years. The book is designed for students with a background in general topology and basic measure theory, but it also includes advanced topics that may appeal to more specialized readers. The content is divided into three parts: Part I covers the elementary theory of general topological vector spaces, including linear spaces, topological vector spaces, completeness, and inductive linear topologies. Part II delves into the duality theory for locally convex spaces, discussing dual pairings, weak topologies, continuous convergence, and related topics. Part III focuses on tensor products and nucularity, exploring projective and injective tensor products, classes of operators, and the approximation property. Key topics include the Hahn-Banach theorem, the Krein-Milman theorem, the Riesz representation theorem, barrelled spaces, reflexive spaces, and nuclear spaces. The book also introduces new perspectives on certain well-known concepts, such as local convergence and Schwartz spaces, and provides a detailed treatment of bornological and ultrabornological spaces. The preface outlines the book's structure, references, and the author's intentions, emphasizing the book's systematic approach and its contributions to the field. The author acknowledges the valuable suggestions and support received from colleagues and publishers, and expresses gratitude to his family for their encouragement and assistance during the writing process.