Metagraphs and their Applications is a presentation of metagraph theory and its applications that begins by defining a metagraph and its uses. They are more complex than a simple graph structure, but they allow for representation and analysis of more complex systems. The material contained in this book is presented in two parts. The first develops the theoretical results with the emphasis on the development of a metagraph algebra. In the second part of the book, four promising applications of metagraphs are examined: 1) modeling of data relations, 2) the modeling of decision models, 3) the modeling of decision rules, and 4) the modeling of workflow tasks. Hence, the theoretical results in the initial chapters lay the foundation for the application areas in the second part of the book. The book concludes by examining several possible extensions of this work.