This book, authored by Hans Reiter and Jan D. Stegeman, is a comprehensive treatise on classical harmonic analysis and locally compact groups. It begins with an introduction to classical harmonic analysis, covering topics such as the algebra \( L^1(\mathbb{R}^n) \), Fourier transforms, and Wiener's theorem. The authors then delve into function algebras and the generalization of Wiener's theorem, exploring topological function algebras and Ditkin sets. The book also discusses locally compact groups and the Haar measure, including integration on these spaces and the properties of \( L^1 \)-spaces. Further chapters focus on locally compact abelian groups, duality theory, and the foundations of harmonic analysis. The text includes detailed sections on functions on these groups, Wiener's theorem, and the spectrum, along with applications. The book concludes with additional material on quasi-invariant measures, invariant convex hulls, and the structure of groups with specific properties.This book, authored by Hans Reiter and Jan D. Stegeman, is a comprehensive treatise on classical harmonic analysis and locally compact groups. It begins with an introduction to classical harmonic analysis, covering topics such as the algebra \( L^1(\mathbb{R}^n) \), Fourier transforms, and Wiener's theorem. The authors then delve into function algebras and the generalization of Wiener's theorem, exploring topological function algebras and Ditkin sets. The book also discusses locally compact groups and the Haar measure, including integration on these spaces and the properties of \( L^1 \)-spaces. Further chapters focus on locally compact abelian groups, duality theory, and the foundations of harmonic analysis. The text includes detailed sections on functions on these groups, Wiener's theorem, and the spectrum, along with applications. The book concludes with additional material on quasi-invariant measures, invariant convex hulls, and the structure of groups with specific properties.