Textbook in PDF format The aim of this book is to provide a comprehensive introduction to solving large systems of equations. In addition to direct algorithms, it presents a wide range of classical and modern solvers – from splitting methods and multigrid techniques to current Krylov subspace methods (CG, GMRES, BiCGSTAB, etc.). These methods are discussed both mathematically and in terms of their practical applications. The book also offers an in-depth treatment of preconditioning techniques to accelerate existing methods. The book covers all the necessary fundamentals, making it highly suitable for self-study. The presentation of the derived algorithms allows for straightforward implementation in any programming language. Detailed MatLAB implementations of common Krylov methods are included in the appendix. Solutions and additional materials are available online