The authors take an inclusive view of the subject and present a broad selection of topics. These range from traditional classics, such as the characterization of line graphs by eigenvalues, to more unusual areas, such as geometric embeddings of graphs and the study of graph homomorphisms. The authors' goal has been to develop each topic in a self-contained fashion, presenting the main tools and ideas with an emphasis on their use in understanding concrete examples. A substantial proportion of the book covers topics that have not appeared in book form before. It provides an accessible introduction to the research literature and crucial open question in modern algebraic graph theory." "This book primarily aims at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general. However, all the necessary graph theory is developed from scratch, so the only prerequisite is a first course in linear algebra and a small amount of elementary group theory. Thus, it should also be accessible to motivated upper-level undergraduates.