In general, I am in complete agreement with those critical but supportive reviews below. As popular science, HUGIS is mediocre. Up to the last few chapters, in which Levin discusses her own scientific interests and contributions, the exposition is far inferior to other popular works on cosmology/relativity. (Among those which Levin cites at the beginning of her book I would single out Kip Thorne's Black Holes... as an exemplary introduction to the field, and a hugely entertaining piece of writing).
When, in due course, Levin does turn to her work -- topology -- HUGIS does get interesting. The book would have been much better, in my view, had Levin devoted the greater part of it to topology, and had she done so at greater depth. That said, the final chapters of HUGIS introduced me to a range of ideas I had not encountered before. I am very eager to learn more about Levin's and others' work in this highly abstruse subfield of astrophysics.
Science aside, a not insubstantial portion of HUGIS is taken up with various personal matters, mostly to do with Levin's (then) difficult relationship with a musician named Warren and her/their anguish about professional/geographic moves. Had the personal material in HUGIS had more to do with Levin's experiences as a scientist, a female scientist, etc., it would have greatly enriched her book and made the conceit of a book-as-a-series-of-letters worthwile. As it stands, however, the personal material in HUGIS was largely uninteresting and irrelevant, and transitions between Levin's personal reflections and her reflections on science were often forced and trite.
All that said, HUGIS is a quick and easy read. It is a decent and gentle introduction to some very difficult concepts. For those readers with little scientific background, it is a fine, abeit light, overview. For those with a deeper background, HUGIS has little to offer save for a sketchy but tantalizing introduction to the work (topology) with which Levin is mostly (and most passionately) engaged.
Another reviewer suggests that Levin had the makings of an excellent book, in HUGIS, had her editor only pushed her further. I agree. HUGIS is a respectable first foray into popular science writing. Here's hoping Levin continues to write and that she matures as a writer. I think she has tremendous potential.