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I am looking for a book that is regarded as the 'classics' of the field.

For example,

  • Algebraic Number theory - Cassels Frohlich
  • Complex analysis - Ahlfors
  • Category Theory - MacLane
  • Topology - Munkres

What are the classical books of other fields such as fourier analysis, set theory, or differential equation?

I am making a comprehensive list of mathematical classics, so the book of any field is welcomed.

SU Lee
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  • Halmos' Naive Set Theory – J. W. Tanner Jul 05 '21 at 02:55
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    FYI, an earlier question that was similar was closed as opinion-based. It's also a very broad question that's not amenable to a single best answer, so at minimum (if it remains open) it should probably be a community wiki. That said, for Fourier analysis, certainly Zygmund's Trigonometric Series would qualify, as would anything by Elias Stein on the topic. –  Jul 05 '21 at 02:58
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    These are not necessarily my favorite books, they are just some books that I think are considered to be classics. Real analysis: baby Rudin; measure theory: Royden, also Rudin; Linear Algebra: Hoffman and Kunze; Differential Topology: Topology from the Differentiable Viewpoint by Milnor; Algebra: Herstein, Artin, Lang; Number Theory: Hardy and Wright; Smooth manifolds: Calculus on Manifolds by Spivak, Analysis on Manifolds by Munkres; Differential Geometry: A Comprehensive Introduction to Differential Geometry by Spivak; Functional analysis: Kreyszig, Rudin; History of Math: Stillwell – littleO Jul 05 '21 at 03:06

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