In 2013, the authors made a fundamental generalization of the T-Q relation by adding an extra "inhomogeneous" term. Most notably, their new methods allow for the systematic exact solution of systems with "off-diagonal" boundaries. This book provides an excellent introduction to the new method of the off-diagonal Bethe Ansatz with applications. This monograph is destined to become a classic in the area and is highly recommended to any researcher with an interest in these topics. ---Prof. Paul A. Pearce, University of Melbourne In 2013, the authors made a significant breakthrough in the field of quantum integrable systems. The simple - yet far reaching - solution proposed by the authors was to introduce an inhomogeneous term in the T-Q equation. The authors proceeded to demonstrate that the off-diagonal Bethe Ansatz method had general applicability, by successfully tackling numerous previously-unsolved models. This volume provides an accessible exposition of this approach, which is likely to have an enduring impact. --- Prof. Rafael Nepomechie, University of Miami This book provides a detailed treatment of the off-diagonal Bethe Ansatz method, with special attention given to the inhomogeneous T-Q relation pioneered recently by the authors. We find the book worthy of special attention. ---Prof. J. H. H. Perk & Prof. H. Au-Yang, Oklahoma State University ...In this book the authors outline the approach for obtaining the eigenvalue spectrum of these models in terms of their off-diagonal Bethe Ansatz method. This method overcomes the problem of not having an obvious reference state, which has long been the stumbling block for solving this class of models. The authors provide a pedagogic and extensive account, treating a number of key models. All these ingredients add up to a classic new book in a fundamentally important area of physics. ---Prof. Murray Batchelor, Chongqing University & Australian National University
