Percolation theory for mathematicians by Harry Kesten is a research monograph that presents rigorous proofs of some basic results in percolation theory. The book is intended for mathematicians and includes a variety of problems that are easy to state but require new methods to solve. It is written for graduate students with a standard probability course background. The book covers a wide range of topics, including periodic graphs, matching pairs, planar modifications, separation theorems, covering graphs, dual graphs, periodic percolation problems, increasing events, bounds for the distribution of #W, the RSW theorem, power estimates, the nature of the singularity at PH, inequalities for critical probabilities, and the resistance of random electrical networks. The book also includes unsolved problems and a comprehensive list of references, author index, subject index, and index of symbols. The author acknowledges the support of the National Science Foundation and the Japan Society for the Promotion of Science. The book is part of the Progress in Probability and Statistics series, edited by P. Huber and M. Rosenblatt. The book is written in English and is published by Springer Science+Business Media New York in 1982. The book is also available in an eBook format. The book is a valuable resource for mathematicians interested in percolation theory and related areas.Percolation theory for mathematicians by Harry Kesten is a research monograph that presents rigorous proofs of some basic results in percolation theory. The book is intended for mathematicians and includes a variety of problems that are easy to state but require new methods to solve. It is written for graduate students with a standard probability course background. The book covers a wide range of topics, including periodic graphs, matching pairs, planar modifications, separation theorems, covering graphs, dual graphs, periodic percolation problems, increasing events, bounds for the distribution of #W, the RSW theorem, power estimates, the nature of the singularity at PH, inequalities for critical probabilities, and the resistance of random electrical networks. The book also includes unsolved problems and a comprehensive list of references, author index, subject index, and index of symbols. The author acknowledges the support of the National Science Foundation and the Japan Society for the Promotion of Science. The book is part of the Progress in Probability and Statistics series, edited by P. Huber and M. Rosenblatt. The book is written in English and is published by Springer Science+Business Media New York in 1982. The book is also available in an eBook format. The book is a valuable resource for mathematicians interested in percolation theory and related areas.