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This book provides an introduction to the theory of existentially
closed groups, for both graduate students and established
mathematicians. It is presented from a group theoretical, rather
than a model theoretical, point of view. The recursive function
theory that is needed is included in the text. Interest in
existentially closed groups first developed in the 1950s. This book
brings together a large number of results proved since then, as
well as introducing new ideas, interpretations and proofs. The
authors begin by defining existentially closed groups, and
summarizing some of the techniques that are basic to infinite group
theory (e.g. the formation of free products with amalgamation and
HNN-extensions). From this basis the theory is developed and many
of the more recently discovered results are proved and discussed.
The aim is to assist group theorists to find their way into a
corner of their subject which has its own characteristic flavour,
but which is recognizably group theory.
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