Many authors begin their preface by confidently describing how their book arose. We started this project so long ago, and our memories are so weak, that we could not do this truthfully. Others begin by stating why they decided to write. Thanks to Freud, we know that unconscious reasons can be as important as conscious ones, and so this seems impossible, too. Moreover, the real question that should be addressed is why the reader should struggle with this text.
Even that question we cannot fully answer, so instead we offer an explanation for our own fascination with this subject. It offers the pleasure of seeing many unexpected and useful connections between two beautiful, and apparently unrelated, parts of mathematics: algebra and graph theory. At its lowest level, this is just the feeling of getting something for nothing. After devoting much thought to a graph-theoretical problem, one suddenly realizes that the question is already answered by some lonely algebraic fact. The canonical example is the use of eigenvalue techniques to prove that certain extremal graphs cannot exist, and to constrain the parameters of those that do. Equally unexpected, and equally welcome, is the realization that some complicated algebraic task reduces to a question in graph theory, for example, the classification of groups with BN pairs becomes the study of generalized polygons.