I'm not a mathematical physicist---I work in quantum computing theory, which <i>maybe</i> is sort of close if you squint?  FWIW, I read the first few chapters of Maudlin's new book and liked them a lot.  I remember taking topology as an undergrad and thinking, "why is everything based around 'open sets,' which can be chosen totally arbitrarily except that they have to be closed under unions and finite intersections?"  I mean, yes, you can build up a theory on that basis and it works very well.  But the notion of open set never impressed itself on me as intuitively central, the way most other basic mathematical notions did---especially given that one can easily define "open sets" (for example, in finite spaces) that have nothing whatsoever to do with the intuitive concept of "openness" that supposedly motivated the definition in the first place.  So I wondered: would it be possible to build up topology on some completely different basis?  This is the main question that Maudlin sets out to answer (affirmatively) in this book.  And it's a big undertaking, and one that many people will probably regard as quixotic and unnecessary <i>even if it succeeds</i>---which might be why no one tried it before (or maybe they did; I can't say for certain about that).  In the preface, Maudlin compares his situation to that of someone who realizes that the Empire State Building would've been better if it had been built a few feet to the left: even if that's true, it's far from obvious that it's worth the effort <i>now</i> to move the thing!  But I, for one, am happy to see someone probe the foundations of topology in this way---especially someone who writes as clearly as Maudlin, so that I can actually understand where he's going and why.

Physics won't be covered until the second volume.  I honestly don't know yet whether there are any real applications to physics, but <i>if</i> there are, one could regard them as just the icing.