The main focus of this book is the new mathematical methods and results of the author and others which have made it possible to put the treatment of the Ising model in a mathematically rigorous framework. Understanding certain exactly solvable models in statistical mechanics and quantum field theory from a mathematical physics perspective is a very important and active area of research. At the heart is the Ising model. The work is useful for graduate students, mathematicians, and physicists interested in the mathematics of statistical mechanics and quantum field theory.