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See pages 107 and following of Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics (second edition)

• Dedekind and the set-theoretical approach
  1. The algebraic origins of Dedekind's set theory, 1856-58
  2. A new fundamental notion for algebra: fields
  3. The emergence of algebraic number theory
  4. Ideals and methodology
  5. Dedekind's infinitism
  6. The diffusion of Dedekind's views