This book provides a detailed account of bosonization, a powerful nonperturbative approach to many-body systems. The first part examines the technical aspects of bosonization, covering topics such as one-dimensional fermions, the Gaussian model, conformal theories, Bose-Einstein condensation, non-Abelian bosonization, and the Ising and WZNW models. The second part discusses applications of bosonization to realistic models, including the Tomonaga-Luttinger liquid, spin liquids in one dimension, and the spin-1/2 Heisenberg chain. The third part addresses quantum impurities, covering potential scattering, the X-ray edge problem, impurities in Tomonaga-Luttinger liquids, and the multi-channel Kondo problem. The book is an excellent reference for researchers and graduate students in theoretical physics, condensed matter physics, and field theory. The book explores the theory of strongly correlated low-dimensional systems, where parallels between high energy and condensed matter physics are especially strong. It discusses the history, main concepts, and ideas of this discipline, as well as the features that excite interest in different communities of physicists. Strongly correlated systems are those that cannot be described as a sum of weakly interacting parts, making them among the most difficult problems in physics. The book explains how bosonization can be used to reformulate complicated interacting models into weakly interacting ones, providing a powerful tool for understanding these systems. The book also discusses the spin-1/2 Heisenberg chain, which provides the first example of 'particles transmutation'—a situation where low-energy excitations of a many-body system differ drastically from the constituent particles. It explains how bosonization can be used to describe such systems, and how it has led to a radical simplification of the theory of strong interactions in (1+1)-dimensions. The book also discusses the discovery of particles with fractional quantum numbers, such as spinons in the antiferromagnetic Heisenberg chain. It also covers non-Abelian bosonization, conformal field theory, and their applications to various models. The book concludes with a discussion of the structure and style of the book, and its aim to bridge the gap between the mathematics of strongly correlated systems and their applications.This book provides a detailed account of bosonization, a powerful nonperturbative approach to many-body systems. The first part examines the technical aspects of bosonization, covering topics such as one-dimensional fermions, the Gaussian model, conformal theories, Bose-Einstein condensation, non-Abelian bosonization, and the Ising and WZNW models. The second part discusses applications of bosonization to realistic models, including the Tomonaga-Luttinger liquid, spin liquids in one dimension, and the spin-1/2 Heisenberg chain. The third part addresses quantum impurities, covering potential scattering, the X-ray edge problem, impurities in Tomonaga-Luttinger liquids, and the multi-channel Kondo problem. The book is an excellent reference for researchers and graduate students in theoretical physics, condensed matter physics, and field theory. The book explores the theory of strongly correlated low-dimensional systems, where parallels between high energy and condensed matter physics are especially strong. It discusses the history, main concepts, and ideas of this discipline, as well as the features that excite interest in different communities of physicists. Strongly correlated systems are those that cannot be described as a sum of weakly interacting parts, making them among the most difficult problems in physics. The book explains how bosonization can be used to reformulate complicated interacting models into weakly interacting ones, providing a powerful tool for understanding these systems. The book also discusses the spin-1/2 Heisenberg chain, which provides the first example of 'particles transmutation'—a situation where low-energy excitations of a many-body system differ drastically from the constituent particles. It explains how bosonization can be used to describe such systems, and how it has led to a radical simplification of the theory of strong interactions in (1+1)-dimensions. The book also discusses the discovery of particles with fractional quantum numbers, such as spinons in the antiferromagnetic Heisenberg chain. It also covers non-Abelian bosonization, conformal field theory, and their applications to various models. The book concludes with a discussion of the structure and style of the book, and its aim to bridge the gap between the mathematics of strongly correlated systems and their applications.