A companion volume to Weaver's Applications of Discrete and Continuous Fourier Analysis (Wiley, 1983), this book addresses the theoretical and analytical aspects of Fourier analysis, including topics usually found only in more advanced treatises. It provides background information before going on to cover such topics as convergence of sequences of Lebegue integral functions, existence of the inner product, Fourier series representation of complex functions, properties and behavior of the Fourier transform, physical interpretation of convolution, the fast Fourier transform, sampling a function, and much more. Exercises, problems, applications, over 150 illustrations, and a Fourier transform FORTRAN subroutine, are included. This volume will be of benefit to applied mathematicians and engineers.