Fourier transform is an efficient method and a powerful tool for solving certain types of differential and integral equations. It is frequently applied for attaining the solutions to the problems of science and engineering such as image analysis, image filtering, image reconstruction, image compression, signal analyzing and circuit analysis. This transform is also effectively applied to initial and boundary value problems. This book is to explore the basic concepts of Fourier transforms in a simple, systematic and easy-to-understand manner. The present book is divided into six chapters that cover all the important topics like Fourier transform, Fourier sine transform, Fourier cosine transform, finite Fourier sine transform, finite Fourier cosine transform and application of Fourier transforms.