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Surveys the history of modern model theory, emphasizing the significance, both for philosophy and for mathematical practice, of its mid-twentieth century transformation. Rich in both context and technical detail, this book will appeal to those working on the history and philosophy of mathematics.

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This book introduces first order stability theory, organized around the spectrum problem, with complete proofs of the Vaught conjecture for ω-stable theories.

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Classification theory: 1985.- Concrete representations of lattices and the fundamental order.- The classification of small weakly minimal sets I.- Orthogonality of types in separably closed fields.- Countable or ?1-like models of Presburger's arithmetic.- An exposition of OTOP.- Exercises on Local Weight.- Locally modular regular types.- Choosing elements in a saturated model.- Degrees of models with prescribed Scott set.- Shrinking, stretchin...