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I have poor university mathematical education, but Math fascinates me, so I decided to educate myself for a bit. I know there is a dozen modern mathematical fields I know nearly nothing about like differential and abstract topology, differential and abstract geometry, homological algebra, Lie groups etc.

I am looking for some books, but not deep textbooks, something like "for dummies" which will spell these fields out, with not very many proofs, not very many abstract symbols. I know there's Roger Penrose — The Road to Reality, the first half of which covers modern differential geometry very well, I know there's Charles Nash, Siddhartha Sen — Topology and Geometry for Physicists, which tries to cover the beginning of abstract topology. Is there anything like that? Thank you.

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You can get started with Topology without Tears found online here.

And sometimes I personally find it fun to soak up smattering of knowledge from biography. So perhaps, you can start with bios of Zariski or Felix Klein?

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I recommend this topology books 1-Topology General-Serie Shawn 2-Topology-REA Problem Solver

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    $\begingroup$ Could you include some information, in the answer, on how these books are an answer to the OP's question? $\endgroup$ – Paul Plummer Mar 30 '15 at 2:26

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