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despite the numerous replies here is masterpiece yet to be mentioned :

Alain Connes' Noncommutative Geometry

This is a most brilliant introduction and overview of many modern aspects in all of the areas

  • Analysis (in particular algebraic)
  • Geometry (in particular algebraic, non commutative and infinite dimensional)
  • Topology (in particular algebraic and analytic)
  • Statistical Physics and Quantum Theory

It is simply just perfect in every aspect - the pedagogical style, graphical design and illustrations, historical side notes .... but most of all ... the originality of the mathematical thought!

Post Made Community Wiki by Raphael Albrecht