For the last few decades researchers from different fields gather their findings and knowledge trying to give a shape to the new science of complex systems. To address this problem, new tools and methods have to be established. A new, or more precisely an alternative, framework for the characterization of complex system was proposed. In this book we will introduce the applicability of applicability of simplicial complexes in the science of complex systems. After introducing the main definitions and properties of simplicial complexes necessary for representation and analysis of complex systems, we will illustrate the usefulness and versatility of tools and concepts related to the simplicial complexes.