Fourier Analysis and Its Applications Introduction Preparations Laplace and Z Transforms Fourier Series L^2 Theory Separation of Variables Fourier Transforms Distributions Multi Dimensional Fourier Analysis Appendix A: The ubiquitous convolution Appendix B: The Discrete Fourier Transform Appendix C: Formulae Appendix D: Answers to exercises Appendix E: Literature. This book presents the basic ideas in Fourier analysis and its applications to the study of partial differential equations. It also covers the Laplace and Zeta transformations and the fundaments of their applications. The author has intended to make his exposition accessible to readers with a limited background for example those not acquainted with the Lebesgue integral or with analytic functions of a complex variable. At the same time he has included discussions of more advanced topics such as the Gibbs phenomenon distributions Sturm Liouville theory Cesaro summability and multi dimensional Fourier analysis topics which one usually will not find in books at this level. Many of the chapters end with a summary of their contents as well as a short historical note. The text contains a great number of examples as well as more than 350 exercises. In addition one of the appendices is a collection of the formulas needed to solve problems in the field. Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University Sweden.