Algebraic graph theory is a fascinating subject concerned with theinterplay between algebra and graph theory. Algebraic tools can beused to give surprising and elegant proofs of graph theoretic facts,and there are many interesting algebraic objects associated withgraphs. The authors take an inclusive view of the subject, andpresent a wide range of topics. These range from standard classics,such as the characterization of line graphs by eigenvalues, to moreunusual areas such as geometric embeddings of graphs and the study ofgraph homomorphisms. The authors' goal has been to present each topicin a self-contained fashion, presenting the main tools and ideas, withan emphasis on their use in understanding concrete examples. Asubstantial proportion of the book covers topics that have notappeared in book form before, and as such it provides an accessibleintroduction to the research literature and to important openquestions in modern algebraic graph theory.This book is primarily aimed at graduate students and researchers ingraph theory, combinatorics, or discrete mathematics in general.However, all the necessary graph theory is developed from scratch, sothe only pre-requisite for reading it is a first course in linearalgebra and a small amount of elementary group theory. It should beaccessible to motivated upper-level undergraduates.Chris Godsil is a full professor in the Department of Combinatorics and Optimization at the University of Waterloo. His main research interestslie in the interactions between algebra and combinatorics, in particularthe application of algebraic techniques to graphs, designs and codes.He has published more than 70 papers in these areas, is a foundingeditor of "The Journal of Algebraic Combinatorics" and is the author ofthe book "Algebraic Combinatorics".Gordon Royle teaches in the Department of Computer Science & SoftwareEngineering at the University of Western Australia. His main researchinterests lie in the application of computers to combinatorialproblems, in particular the cataloguing, enumeration and investigationof graphs, designs and finite geometries. He has published more than30 papers in graph theory, design theory and finite geometry.