This edition of the book not only covers the basic fourier theory and applications but also includes their fourier mapping and also its deployment in signal processing by way of the discrete fourier transform theorem in more logical manner for senior undergraduates or graduates students and also researchers or academician of mathematical science, computer science, numerical analysis, physics and other allied disciplines of science and engineering. The book commences with the definition and properties of fourier series, discrete and fourier transform. A basic knowledge of fourier series, transform in initial chapters is important to build in understanding the digital calculation of both series and transform and its various application in remaining chapters. The book is designed to demonstrate the recent applications of fourier analysis in understanding the mechanical and electrical systems as well as the one-dimensional wave equation. At the same time, content has been adapted to keep serving the modern day requirements of intermediate course in mathematics and computer and physics domain. The book stresses on giving its readers experience of applying the fourier analysis in widespread applications which are vigilantly selected based on their importance in both the domain. The fact is that readers of this book belong to a broad spectrum of academic levels and professional scales, so we made enormous efforts to make the content of this book as pleasant as possible for our wide range of readers. Researchers and academicians in universities may use it to extend their studying and teaching material whereas the students may use it for quick understanding of concepts and conceptual plethora about fourier analysis. The organization of concepts throughout the book has been done in such depth that the readers are not required to have prior knowledge of fourier analysis and signal processing. The explanation of ideas and theory and its applications are well understood with the graphical and mathematical representation. In this edition we aim to serve a wide range of readers groups with the intention of contributing towards advancement in the field of fourier analysis. The book will certainly help students and researchers in building a strong foundation in dynamics of continuous and discrete fourier analysis systems along with assisting professors in making students understand the theories, concepts and its application in much-enhanced way.