This course provides introduction into Fourier transform. It consists of review of essential mathematics required for good understanding of Fourier integral and introduction into Fourier Transform properties and pairs. Course includes slides, two sets of problem assignment and their solutions in Adobe Acrobat format. Why I decided to prepare this course? There are hundreds of textbooks covering this material, however they often concentrate on complicated mathematical details and do not explain things clearly. The essential part – understanding of basic Fourier transform principles is often difficult to find. I spent many years working in signal and image processing, published a lot of papers, patents and books, and I always came to conclusion that simple solutions can be found for any problem. So this course is an attempt to explain this material for somebody who has little experience in the area, but wants to understand how things work. First section of this course explains concepts of trigonometric functions, derivatives and integrals, power series, exponential and complex exponential. I tried to make presentation clear and simple, avoiding complicated details and concentrating on understanding main concepts. Second section starts from introduction of Integral Fourier transform. I described properties of Fourier transform and their application to engineering and communication problems, including convolution, cross-correlation, modulation and demodulation etc. I hope this course will provide fundamental knowledge base for analysis of linear systems, filtering, sampling and more advanced topics in signal processing and analysis. Course include pdf version of powerpoint slides, problem assignments and solutions.