This book explores the connection between random walks and electric networks, using concepts from probability theory and electrical engineering. It begins with a one-dimensional random walk, showing how it relates to electric circuits and harmonic functions. The authors then extend this to two-dimensional random walks, discussing harmonic functions, the Dirichlet problem, and the uniqueness principle. They also introduce the method of relaxations for solving Dirichlet problems and the use of Markov chains to analyze random walks on graphs. The book emphasizes the deep relationship between random walks and electric networks, using electrical concepts like current and voltage to understand probabilistic behavior. It also discusses the importance of Rayleigh's method in proving results about random walks and electric networks, and highlights the role of harmonic functions in both fields. The text is written for readers with a basic understanding of probability theory, linear algebra, and electric network theory, and provides exercises to reinforce key concepts. The authors conclude by showing how random walks can be used to solve problems in probability and electrical engineering, and how these two fields are deeply interconnected.This book explores the connection between random walks and electric networks, using concepts from probability theory and electrical engineering. It begins with a one-dimensional random walk, showing how it relates to electric circuits and harmonic functions. The authors then extend this to two-dimensional random walks, discussing harmonic functions, the Dirichlet problem, and the uniqueness principle. They also introduce the method of relaxations for solving Dirichlet problems and the use of Markov chains to analyze random walks on graphs. The book emphasizes the deep relationship between random walks and electric networks, using electrical concepts like current and voltage to understand probabilistic behavior. It also discusses the importance of Rayleigh's method in proving results about random walks and electric networks, and highlights the role of harmonic functions in both fields. The text is written for readers with a basic understanding of probability theory, linear algebra, and electric network theory, and provides exercises to reinforce key concepts. The authors conclude by showing how random walks can be used to solve problems in probability and electrical engineering, and how these two fields are deeply interconnected.