S-parameters and transmission lines are the main tools utilized in microwave amplifier design. Before we can design our own circuits, however, we need to study some methods of analysis. In this chapter, we will use mathematical and graphical tools to analyze circuits. These circuits will be networks composed of one or more elements. The methods shown in this chapter assume that the S-parameters of a one or two-port have been found or measured. We will concentrate on analyzing the circuit response of a network and groups of interconnected networks. The tools presented in this chapter as well as in Chapter 3 lay the groundwork for the following chapters on synthesizing microwave circuits and amplifiers.