The chapter introduces the fundamental concepts and analysis methods in power system analysis, focusing on steady-state and dynamic conditions. It emphasizes the complexity and interdependence of the power system, which is often referred to as the largest and most complex machine ever built by humans. The chapter discusses the transmission of electric power as a three-phase signal, where balanced currents sum to zero, and the assumption of balanced voltages to maintain constant total power transmission. The steady-state analysis section covers the operation of the power system under stable conditions, where transients from disturbances are assumed to have settled. Key aspects include economic operation, reliability, and power flow analysis. The chapter details the modeling of key components such as transformers, transmission lines, generators, and loads, providing detailed mathematical formulations and circuit models. The power flow analysis section explains the fundamental equations that balance power flow in the system, including real and reactive power flows. It discusses the nonlinear nature of these equations and the computational challenges they pose, particularly in large-scale systems. The chapter introduces several algorithms for solving these equations, including the Gauss-Seidel algorithm, the Newton-Raphson algorithm, and the fast decoupled power-flow algorithm. Each algorithm is described in detail, highlighting their strengths and weaknesses in terms of convergence speed and computational complexity. Overall, the chapter provides a comprehensive overview of the theoretical and practical aspects of power system analysis, emphasizing the importance of accurate modeling and efficient solution methods for ensuring the reliable and efficient operation of power systems.The chapter introduces the fundamental concepts and analysis methods in power system analysis, focusing on steady-state and dynamic conditions. It emphasizes the complexity and interdependence of the power system, which is often referred to as the largest and most complex machine ever built by humans. The chapter discusses the transmission of electric power as a three-phase signal, where balanced currents sum to zero, and the assumption of balanced voltages to maintain constant total power transmission. The steady-state analysis section covers the operation of the power system under stable conditions, where transients from disturbances are assumed to have settled. Key aspects include economic operation, reliability, and power flow analysis. The chapter details the modeling of key components such as transformers, transmission lines, generators, and loads, providing detailed mathematical formulations and circuit models. The power flow analysis section explains the fundamental equations that balance power flow in the system, including real and reactive power flows. It discusses the nonlinear nature of these equations and the computational challenges they pose, particularly in large-scale systems. The chapter introduces several algorithms for solving these equations, including the Gauss-Seidel algorithm, the Newton-Raphson algorithm, and the fast decoupled power-flow algorithm. Each algorithm is described in detail, highlighting their strengths and weaknesses in terms of convergence speed and computational complexity. Overall, the chapter provides a comprehensive overview of the theoretical and practical aspects of power system analysis, emphasizing the importance of accurate modeling and efficient solution methods for ensuring the reliable and efficient operation of power systems.