For the last few decades researchers from different fields gather their findings andknowledge trying to give a shape to the new science of complex systems. To address thisproblem， new tools and methods have to be established. We propose a new， or more precisely analternative， framework for the characterization of complex system. In this book we will give anintroduction of applicability of simplicial complexes in the science of complex systems. Afterintroducing of main definitions and properties of simplicial complexes necessary forrepresentation and analysis of complex systems， we will illustrate the usefulness and versatilityof tools and concepts related to the simplicial complexes. In the broad sense the exposition willcover several typical manifestations of complex systems， that is， emerging psychological spaceof opinions and their exchange， topological description of complex networks， and topologicalinvariability in dynamical systems. This book sets a stage and serves as a starting point toinspire readers. This is always the authors' intention and wish.
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