This chapter deals with the analysis of power systems. Power system analysis is concerned with understanding the operation of the system as a whole. Generally, the system is analyzed either under steady-state operating conditions or under dynamic conditions during disturbances. The primary analysis tool for steady-state operation is the so-called power flow analysis, where the voltages and power flow through the system are determined. This analysis is used for both operation and planning studies and throughout the system at both the high and low transmission voltages. This chapter introduces the basic concepts in power system analysis, namely modeling issues, power flow studies, and dynamic stability analysis. The concepts are illustrated on simple power system representations. In real power systems, power-flow studies and system stability studies are routinely carried out for enduring the reliability and security of the electric grid separation. While the basic concepts are summarized in this chapter on simple examples, the real power systems are large-scale, nonlinear systems. The large interconnected nature of electric networks makes the computation aspects highly challenging.