The chapter discusses the relationship between random walks and electric networks, focusing on Polya's theorem that a random walker on an infinite street network in two dimensions will return to the starting point, while in three or more dimensions, there is a positive probability of escaping to infinity. The authors use Rayleigh's method, originally introduced by Lord Rayleigh for investigating musical instruments, to prove this theorem. They also explore the connection between random walks and harmonic functions, demonstrating that the probability of reaching a boundary point in a random walk is determined by the values of a harmonic function at that point. The chapter includes exercises that apply these concepts to specific problems, such as finding the probability of reaching a boundary point in a random walk and solving Dirichlet problems using various methods, including Monte Carlo simulation, the method of relaxations, and linear equations.The chapter discusses the relationship between random walks and electric networks, focusing on Polya's theorem that a random walker on an infinite street network in two dimensions will return to the starting point, while in three or more dimensions, there is a positive probability of escaping to infinity. The authors use Rayleigh's method, originally introduced by Lord Rayleigh for investigating musical instruments, to prove this theorem. They also explore the connection between random walks and harmonic functions, demonstrating that the probability of reaching a boundary point in a random walk is determined by the values of a harmonic function at that point. The chapter includes exercises that apply these concepts to specific problems, such as finding the probability of reaching a boundary point in a random walk and solving Dirichlet problems using various methods, including Monte Carlo simulation, the method of relaxations, and linear equations.