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Kurzbeschreibung Despite the large research effort in both public and commercial companies, no textbook has yet been written on Carbon Capture and Storage (CCS). This book provides an overview, examining the dominant processes as well as the mathematical and numerical methods necessary to analyze the relevant systems. It provides an introduction to single-phase and multi-phase flow in porous media, including the most common mathematical analyses, and an overview of numerical methods for the equations. A considerable part of the book discusses appropriate modeling scales, including how to formulate consistent governing equations at these scales.