The book provides an introduction to fundamental concepts and basic theorems of graph theory. Graphs are presented as modeling tools for various applications in the fields of location planning, logistics, traffic planning, scheduling, and the design of communication networks. Efficient methods are introduced and rigorously analyzed for the resulting graph-theoretical problems. For complexity-theoretically "difficult" problems, the book includes efficient approximation methods that quickly deliver solutions with provable quality. This introduction to fundamental concepts and basic theorems of graph theory features not only classical results but also the latest findings and topics such as dynamic flows, which have previously been overlooked in textbooks. The presentation, enriched with numerous illustrations, facilitates understanding and enhances motivation for the reader.