This book provides essential lecture notes on solving large linear
saddle-point systems, which arise in a wide range of applications and
often pose computational challenges in science and engineering. The
focus is on discussing the particular properties of such linear systems,
and a large selection of algebraic methods for solving them, with an
emphasis on iterative methods and preconditioning. The theoretical
results presented here are complemented by a case study on potential
fluid flow problem in a real world-application. This book is mainly
intended for students of applied mathematics and scientific computing,
but also of interest for researchers and engineers working on various
applications. It is assumed that the reader has completed a basic course
on linear algebra and numerical mathematics.