This Topic seeks to expand our understanding of Fourier Series. First, through an example, the Topic considers the general form or structure of the trigonometric Fourier series, and what is a valid Fourier Series and what isn't. Second, the Topic considers the notion of signal approximation through the truncated Fourier Series, where only a finite number of harmonics are used rather than an infinite number. To quantify the goodness-of-fit of the approximation, the power of the error signal is considered as a function of the number of harmonics, where it is seen this power drops monotonically. The Topic introduces the idea of an acceptable level of error, and discusses the application of this in Image Compression and other signal compression algorithms.