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Fourier Analysis has now become a widely used technique in many branches of science and engineering. This book has been written mainly with the needs of students of these subjects in mind. Thus full mathematical rigour has not been attempted. On the other hand an attempt has been made to avoid presenting the subject in such a way that it becomes a mere "tool". An elementary proof of the fundamental theorems has been given to provide some insight into the more theoretical aspects of the subject and to provide a better basis for the understanding of some of the phenomena which occur later, such as the Gibbs’ phenomenon. The first two chapters deal with Fourier Series. These are followed by two on Fourier Integrals and finally two on applications. It is common to think of Fourier Analysis in terms of the analysis of time varying functions. The final chapter shows that this point of view is unnecessarily restricted and that the theory is of much wider applicability