This book provides a thorough introduction to the fascinating world of phase transitions as well as many related topics, including random walks, combinatorial problems, quantum field theory and S-matrix. Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry, and anomalous dimensions, have deeply changed the modern vision of many areas of Physics, leading to remarkable
developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides an excellent introduction to frontier topics of exactly solved
models in statistical mechanics and quantum field theory, renormalization group, conformal models, quantum integrable systems, duality, elastic S-matrix, thermodynamics Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics, distinguished for their elegance and beauty, such as infinite dimensional algebras, conformal mappings, integral equations or modular functions.