The emphasis of this text is the broad field of Fourier analysis and some of its immediate outgrowths including convolution, systems theory, Shannon sampling theory and the modelling of random variables and stochastic processes. The contents of this book evolved from a set of lecture notes for courses in advanced engineering mathematics (Chapters 2, 3, 4, 12 and 13), multidimensional signal processing (Chapters 2, 9 and 11), signal reconstruction (Chapters 2, 10 and 11) and Shannon sampling and interpolation theory (Chapters 2, 5, 7, 6 and 7). Chapter 4 is useful as a supplement a graduate course on random variables and stochastic processes. The book is written at the level of the advanced senior or first year graduate student who has an introductory foundation in Fourier analysis and stochastic processes. Rudimentary familiarity with image processing is helpful but not necessary.