The book considers connected and interacting systems that exchange energy, mass, information, etc. in various ways. These kind of systems are referred to as Complex Heterogeneous Systems (CHeSs). The elementary building blocks of CHeSs are based on fundamental thermodynamic principles as well as basic graph-theoretic concepts. It investigates ways of defining complexity, computing percolation thresholds, making smart decisions (also by learning), and identifying battery life, e.g. by blow-up analysis.