This well-written book addresses from the theoretical standpoint the description of one-dimensional systems (mainly interacting fermions). As made clear in the book the field is the object of lively and relevant theoretical and experimental research. Great attention is devoted to a clear organization of the book, essentially divided into a general theoretical treatment and a part on specific models and applications. The author himself gives suggestions in the preface on how to most profitably read the book. In particular in the first three chapters the bosonization technique and the concept of Luttinger liquid, one-dimensional “counterpart” of the Fermi liquid concept, are introduced and explored.
The book is written in a clear style, most often trying to convey the main results without too many details of technicalities. It is however quite dense and a good working knowledge of many-body physics is required in order to actually follow the physical arguments. Similarly when dealing with examples and specific applications a previous knowledge of the considered model (possibly its higher-dimensional counterpart) is certainly useful.