This chapter aims to introduce the fundamental concepts and graphical tools for analyzing time-domain and frequency-domain function contents. It explains how the various representations of their frequency contents are connected to the Fourier series representation of periodic functions in general. The chapter shows that a sum of sinusoidal modes can be expressed in a number of ways. While the various formulas are mathematically equivalent, one form could be more convenient than another depending on the manipulations required for a particular application. Also, it is not uncommon that while one form is more suitable for describing a physical problem, another form is more desirable for a computational purpose. When a cyclic physical phenomenon is described by a cosine curve, the general form used in many applications is the cosine mode with phase shift angle.