To quote a review by W. Ledermann in the Physics Bulletin, 'By skilfully blending the points of view of pure and applied mathematics, of physics, and of numerical methods, Professor Lanczos has succeeded in writing a book on Fourier series which is highly readable and informative. The subject itself is used as a leitmotiv to illuminate and revise the fundamental concepts of analysis ranging from the notion of a function to the method of contour integration.' Originally published in 1966, this well-written and still-cited text covers Fourier analysis, a foundation of science and engineering. The author meticulously develops the topic in a friendly, conversational tone to clarify the material and engage the reader. 161 problems are integrated into the text to walk undergraduate and graduate students of engineering, physics, and mathematics down the simplest path to a solution.