The Wavelet Transform has stimulated research that is unparalleled since the invention of the Fast Fourier Transform and has opened new avenues of applications in signal processing, image compression, radiology, cardiology, and many other areas. This book grew out of a short course for mathematics students at the ETH in Zurich, it provides a solid mathematical foundation for the broad range of applications enjoyed by the wavelet transform. Numerous illustrations and fully worked out examples enhance the book.