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Lecture notes are devoted to the solution of large linear saddle-point systems that arise in a wide variety of applications and often represent a computational challenge in science and engineering. The focus is to discuss particular properties of such linear systems and a large selection of algebraic methods for their solution with emphasis on iterative methods and preconditioning. Theoretical results are complemented with the case study of potential fluid flow problem in real world-application. This book is intended to students of applied mathematics and scientific computing but also to researchers and engineers working in various applications. It is assumed that a potential reader has a knowledge of a basic course in linear algebra and numerical mathematics.