The study of permutation groups has always been closely associated
with that of highly symmetric structures. The objects considered
here are countably infinite, but have only finitely many different
substructures of any given finite size. They are precisely those
structures which are determined by first-order logical axioms
together with the assumption of countability. This book concerns
such structures, their substructures and their automorphism groups.
A wide range of techniques are used: group theory, combinatorics,
Baire category and measure among them. The book arose from lectures
given at a research symposium and retains their informal style,
whilst including as well many recent results from a variety of
sources. It concludes with exercises and unsolved research
problems.
General
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