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.