The book uses a detailed and systematic description of local Fourier k-grid (k=1, 2, 3) analysis for general systems of partial differential equations to provide a framework that answers questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Accompanying software confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes theory important to those who need to delve deeper into the details of the subject. The book consists of two parts. The first part (Chapters 1-4), provides facts that are necessary for understanding basic principles of multigrid and local Fourier analysis and for an efficient use of the accompanying software. The second part (Chapters 5-7), describes the theory used in the software and is important for those readers who want to understand details. Summarizing, the book is intended as a companion to basic multigrid literature with a focus on quantitative convergence estimates, which are crucial for the development of new multigrid software. The volume will be of interest not only to those interested in theory but also to a wide range of practically oriented researchers, not limited to multigrid specialists.