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Currently, I am attempting to learn noncommutative geometry. My interests mostly lie on the boundaries of pure mathematics and theoretical physics, so I am not only interested in the mathematical formulation of the theory, but also in the physical applications.

I am familiar with differential/algebraic topology/particle physics and some basic notions of homological algebra, but am fairly weak in functional analysis.

What books/references/review articles would one recommend as the best or easiest starting point to learning this subject? A book that is the most self-contained/pedagogical? (I am currently starting to read Basic Noncommutative Geometry by Khalkal, but was wondering if there were any books even more suitable for a beginner). As I want to get started with learning NCG as quickly as possible, are there any short review papers, notes, or specific chapters of texts where I can gain a bare minimum of prerequisites such as functional analysis to start reading a book on NCG instead of having to read an entire book on operator algebras before starting my study? Or some books that would be helpful that I could read concurrently?

Thanks!

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  • $\begingroup$ I'd recommend "Noncommutative Geometry and Particle Physics" by van Suijlekom. It doesn't cover a lot of topics a mathematician might be interested in, but from a physicist's perspective it is far easier and more self-contained than other books I've seen. $\endgroup$ – octonion Apr 27 '15 at 9:24
  • $\begingroup$ Thanks! Is that even a better starting point than "an introduction to noncommutative geometry and its physical applications" madore? Also would it allow one to read further ncg books after finishing it? $\endgroup$ – combustion1925 Apr 27 '15 at 13:38
  • $\begingroup$ I haven't looked at Madore so I can't say for sure. The focus of van Suijlekom's book and Khalkhali's is entirely different, and I don't think a more mathematical book will be too much easier after reading. Van Suijlekom focuses on the spectral triple and its connections to gauge theories, and it is very relevant to Connes' recent physics papers for instance. $\endgroup$ – octonion Apr 28 '15 at 1:10
  • $\begingroup$ What would be the best way to prepare for more mathematical books such as Khalkhali's? Van Suijlekom clearly lists the required topics and short references to them, but I can't find similar clear references for the more mathematical books. $\endgroup$ – combustion1925 Apr 28 '15 at 1:13
  • $\begingroup$ I'm not an expert, I'm learning this too. There is good discussion on learning materials in response to this question. I found more mathematical books were easier after learning more about commutative algebras from those sources. Good luck! $\endgroup$ – octonion Apr 28 '15 at 1:21

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