The book "Iterative Solution of Large Sparse Systems of Equations" by Wolfgang Hackbusch, published by Springer, is a comprehensive treatise on the numerical methods for solving large sparse systems of equations. The book is divided into three main parts: Linear Iterations, Semi-Iterations and Krylov Methods, and Special Iterations. **Part I: Linear Iterations** covers the introduction to iterative methods, classical linear iterations, and their analysis. It includes discussions on consistency, convergence, and computational efficiency. Key methods such as Richardson, Jacobi, Gauss-Seidel, and SOR iterations are detailed, along with their block versions and convergence rates. **Part II: Semi-Iterations and Krylov Methods** focuses on semi-iterative methods and Krylov subspace methods. It introduces the Chebyshev method, the conjugate gradient method, and the minimal residual method. The chapter on semi-iterations discusses the application of these methods to various iterative schemes and their numerical examples. **Part III: Special Iterations** explores advanced techniques including multigrid iterations, domain decomposition methods, and hierarchical LU iteration. It also covers tensor-based methods and their applications to solving linear systems and variational problems. The book is designed for readers with a background in analysis and linear algebra, providing detailed mathematical proofs and numerical examples to illustrate the concepts. It is suitable for graduate students, researchers, and professionals in applied mathematics, engineering, and computer science.The book "Iterative Solution of Large Sparse Systems of Equations" by Wolfgang Hackbusch, published by Springer, is a comprehensive treatise on the numerical methods for solving large sparse systems of equations. The book is divided into three main parts: Linear Iterations, Semi-Iterations and Krylov Methods, and Special Iterations. **Part I: Linear Iterations** covers the introduction to iterative methods, classical linear iterations, and their analysis. It includes discussions on consistency, convergence, and computational efficiency. Key methods such as Richardson, Jacobi, Gauss-Seidel, and SOR iterations are detailed, along with their block versions and convergence rates. **Part II: Semi-Iterations and Krylov Methods** focuses on semi-iterative methods and Krylov subspace methods. It introduces the Chebyshev method, the conjugate gradient method, and the minimal residual method. The chapter on semi-iterations discusses the application of these methods to various iterative schemes and their numerical examples. **Part III: Special Iterations** explores advanced techniques including multigrid iterations, domain decomposition methods, and hierarchical LU iteration. It also covers tensor-based methods and their applications to solving linear systems and variational problems. The book is designed for readers with a background in analysis and linear algebra, providing detailed mathematical proofs and numerical examples to illustrate the concepts. It is suitable for graduate students, researchers, and professionals in applied mathematics, engineering, and computer science.