The book "Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions" by Dieter Forster, originally published in 1975, is a comprehensive treatise on the application of correlation functions and linear response theory to the study of non-equilibrium phenomena in various physical systems. The author, a professor of physics at Temple University, aims to provide a unified and elementary account of these concepts, making them accessible to both graduate students and researchers in physics and chemistry. The book covers a wide range of topics, including the hydrodynamic description of spin diffusion, the formal properties of correlation functions, the normal fluid, the memory function formalism, Brownian motion, broken symmetry, hydrodynamic spin waves in ferromagnets and antiferromagnets, superfluids, nematic liquid crystals, and superconductors. Each chapter delves into specific examples and applications, providing detailed derivations and discussions of key concepts such as symmetry properties, positivity, fluctuation-dissipation theorems, sum rules, and Kubo relations. The book emphasizes the importance of correlation functions in describing the dynamical behavior of many-particle systems, particularly in the context of non-equilibrium statistical mechanics. It also highlights the role of collective modes and long-range correlations in systems with broken symmetry, such as ferromagnets and superfluids. The author's goal is to bridge the gap between microscopic equations of motion and macroscopically observable phenomena, offering a common language for understanding a broad spectrum of physical systems. The book is structured to be self-contained and suitable for independent study, as well as for use as a textbook in graduate courses on non-equilibrium statistical mechanics. It includes a detailed bibliography and references to further reading, making it a valuable resource for both students and researchers in the field.The book "Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions" by Dieter Forster, originally published in 1975, is a comprehensive treatise on the application of correlation functions and linear response theory to the study of non-equilibrium phenomena in various physical systems. The author, a professor of physics at Temple University, aims to provide a unified and elementary account of these concepts, making them accessible to both graduate students and researchers in physics and chemistry. The book covers a wide range of topics, including the hydrodynamic description of spin diffusion, the formal properties of correlation functions, the normal fluid, the memory function formalism, Brownian motion, broken symmetry, hydrodynamic spin waves in ferromagnets and antiferromagnets, superfluids, nematic liquid crystals, and superconductors. Each chapter delves into specific examples and applications, providing detailed derivations and discussions of key concepts such as symmetry properties, positivity, fluctuation-dissipation theorems, sum rules, and Kubo relations. The book emphasizes the importance of correlation functions in describing the dynamical behavior of many-particle systems, particularly in the context of non-equilibrium statistical mechanics. It also highlights the role of collective modes and long-range correlations in systems with broken symmetry, such as ferromagnets and superfluids. The author's goal is to bridge the gap between microscopic equations of motion and macroscopically observable phenomena, offering a common language for understanding a broad spectrum of physical systems. The book is structured to be self-contained and suitable for independent study, as well as for use as a textbook in graduate courses on non-equilibrium statistical mechanics. It includes a detailed bibliography and references to further reading, making it a valuable resource for both students and researchers in the field.