The American Mathematical Society has printed a nice, non-technical discussion of some basics of modern topology, necessarily intermingled with a discussion of modern geometry. It’s in the form of a tribute to a highly regarded mathematician who was one of the pioneers of modern topology, William Thurston.
The article is found at: Remembering Bill Thurston (1946-2012).
It’s a good one and might help those without mathematical backgrounds to understand what is behind some of my recent writings including the book: The Shape of Reality.