The Fourier transform is one of the important mathematical tools in a wide variety of science and engineering fields. Its application - as Fourier analysis or harmonic analysis - provides useful decompositions of signals into fundamental ("primitive") components, giving shortcuts in the computation of complicated sums and integrals, and often revealing hidden structure in the data. This text develops the basic definitions, properties and applications of Fourier analysis, the emphasis being on techniques for its application to linear systems, although other applications are also considered. The application of Fourier analysis to a wide variety of signals, including discrete time (or parameter), continuous time (or parameter), finite duration, and infinite duration are discussed in the text.