This book is devoted to the analysis of the structure of complex networks by combining results from algebraic, topological, and extremal graph theory with statistical and molecular physics, as well as with contributions from mathematical chemistry, biology, and social sciences. It is divided into two parts consisting of twelve chapters dedicated to the development of theoretic tools for the structural analysis of networks, and seven chapters illustrating, in a critical way, applications of these tools to real-world scenarios. The first chapters provide detailed coverage of adjacency, metric, and topological properties of networks, followed by chapters devoted to the analysis of fragment-based and global invariants in complex networks. Then, there are chapters that analyse the concepts of communicability, centrality, bipartivity, expansibility, and communities in networks, as well as the study of random networks of different types. The second part of the book starts with an analysis of the study of gene regulation and transcription networks, followed by a chapter dedicated to the study of protein residue networks and another on protein-protein interaction networks. Then, the study of reaction networks is critically presented in three main sections devoted to man-made organic reactions, the chemical reactions in planetary atmospheres, and metabolic networks. This part of the book continues with the study of anatomical networks, which include intercellular, vascular, and brain networks. Another chapter studies the use of complex networks in ecological scenarios by examining not only food webs, but also mutualistic webs and landscape networks. The final chapter of the book is devoted to the study of both social and economic networks.