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!