I bought this a few years ago whilst browsing the now-defunct QI Bookshop in Oxford. Barrow is an author I'd been aware of, but I expected to find this quite heavy going. In fact, it was quite readable, though Barrow definitely writes for an intelligent audience.
Barrow begins by looking at various limits humanity has reached and breached in its history, and also considers what may happen in the future. Some limits are technical; others are economic or political. I can't say I recall him discussing any ethical limits, which is perhaps curious given that he does discuss various philosophical issues in these chapters.
The final third of the book is by far the most interesting, discussing cosmology, time travel, and Gödel, and it's worth reading for these chapters alone. Barrow appears to favour the notion that the Universe may not in fact be complex enough for Gödel's Incompleteness Theorem to apply; but if it does apply to the Universe, then it must be either incomplete, or inconsistent (one possibility would be to permit time-travel paradoxes, for example). Topically, there's also a brief discussion on the Arrow Impossibility Theorem on voting systems, something perhaps to bear in mind in the coming months.