5.1 Introduction5.2 From the Fourier Series to the Fourier Transform5.3 Existence of the Fourier Transform5.4 Fourier Transforms from the Laplace Transform5.5 Linearity, Inverse Proportionality, and Duality5.6 Spectral Representation5.7 Convolution and Filtering5.8 Additional Properties5.9 What have we Accomplished? What is Next?