One: The Emergence of Sets within Mathematics -- I Institutional and Intellectual Contexts in German Mathematics, 1800–1870 -- II A New Fundamental Notion: Riemann’s Manifolds -- III Dedekind and the Set-theoretical Approach to Algebra -- IV The Real Number System -- V Origins of the Theory of Point-Sets -- Two: Entering the Labyrinth — Toward Abstract Set Theory -- VI The Notion of Cardinality and the Continuum Hypothesis -- VII Sets and Maps as a Foundation for Mathematics -- VIII The Transfinite Ordinals and Cantor’s Mature Theory -- Three: In Search of an Axiom System -- IX Diffusion, Crisis, and Bifurcation: 1890 to 1914 -- X Logic and Type Theory in the Interwar Period -- XI Consolidation of Axiomatic Set Theory -- Bibliographical References -- Index of Illustrations -- Name Index.

"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic).