TITLE: Reference request: Book of topology from "Topos" point of view
QUESTION [12 upvotes]: Question: Is there any book of topology in the modern language of topos theory?
Motivation: 

In "Sheaves in Geometry and Logic" Mac Lane and Moerdijk say: "For Grothendieck, topology became the study of (the cohomology of) sheaves, and the sheaves "sited" on a given Grothendieck topology formed a topos - subsequently called a Grothendieck topos". my question is about a book of the study of this idea.
Relations between geometry and logic.

REPLY [19 votes]: "Topology via Logic" is only half way there. It is firmly rooted in classical mathematics and makes no connections with toposes.
Mac Lane and Moerdijk is a good suggestion. As for reading it backwards: that is pretty much the aim of my "Locales and Toposes as Spaces" (Chapter 8 in "Handbook of Spatial Logics" (ed. Aiello, Pratt-Hartman, van Bentham), Springer, 2007, pp. 429-496; ISBN 978-1-4020-5586-7). I wanted to guide the reader through the results in Mac Lane and Moerdijk in an order that brings out the "generalized space" idea of toposes.
I think it's fair to say that all those fall short of bringing out some of the ideas of algebraic topology that motivated Grothendieck in the first place. I don't know any books to recommend that cover that.
Steve Vickers.