This book provides an in-depth exploration of classical harmonic analysis and locally compact groups, authored by Hans Reiter and Jan D. Stegeman. It begins with an overview of harmonic analysis, focusing on the algebra $ L^{1}(\mathbb{R}^{v}) $, Fourier transforms, and Wiener's theorem. The text then delves into function algebras, their generalization of Wiener's theorem, and concepts like Ditkin sets and ideals in function algebras. The following chapters discuss locally compact groups and the Haar measure, essential tools in harmonic analysis. The book then examines locally compact abelian groups, their duality theory, and the foundations of harmonic analysis. It explores functions on these groups, including properties of $ L^{1}(G) $ and the Poisson formula. Wiener's theorem is extended to locally compact abelian groups, with discussions on Segal algebras and Beurling algebras. The text also covers the spectrum and its applications, including sets of spectral synthesis and Ditkin sets on groups. It investigates functions on general locally compact groups, discussing quasi-invariant measures, invariant convex hulls, and properties like $ P_{p} $ and $ (\mathcal{M}) $. The book concludes with additional material, including theorems by Domar, Malliavin, and more on Segal algebras, as well as a summary of notations, references, and a subject index. The content is structured to provide a comprehensive understanding of harmonic analysis within the framework of locally compact groups, offering both theoretical insights and practical applications. It serves as a valuable resource for researchers and students in functional analysis and harmonic analysis.This book provides an in-depth exploration of classical harmonic analysis and locally compact groups, authored by Hans Reiter and Jan D. Stegeman. It begins with an overview of harmonic analysis, focusing on the algebra $ L^{1}(\mathbb{R}^{v}) $, Fourier transforms, and Wiener's theorem. The text then delves into function algebras, their generalization of Wiener's theorem, and concepts like Ditkin sets and ideals in function algebras. The following chapters discuss locally compact groups and the Haar measure, essential tools in harmonic analysis. The book then examines locally compact abelian groups, their duality theory, and the foundations of harmonic analysis. It explores functions on these groups, including properties of $ L^{1}(G) $ and the Poisson formula. Wiener's theorem is extended to locally compact abelian groups, with discussions on Segal algebras and Beurling algebras. The text also covers the spectrum and its applications, including sets of spectral synthesis and Ditkin sets on groups. It investigates functions on general locally compact groups, discussing quasi-invariant measures, invariant convex hulls, and properties like $ P_{p} $ and $ (\mathcal{M}) $. The book concludes with additional material, including theorems by Domar, Malliavin, and more on Segal algebras, as well as a summary of notations, references, and a subject index. The content is structured to provide a comprehensive understanding of harmonic analysis within the framework of locally compact groups, offering both theoretical insights and practical applications. It serves as a valuable resource for researchers and students in functional analysis and harmonic analysis.