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.
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?