This superb survey of the study of mathematical structures details how both model theoretic methods and permutation theoretic methods are useful in describing such structures. In addition, the book provides an introduction to current research concerning the connections between model theory and permutation group theory. Comprised of a collection of articles--some introductory, some more in-depth, and some containing previously unpublished research--the book will prove invaluable to graduate students meeting the subject for the first time as well as to active researchers studying mathematical logic and permutation group theory.