This is effectively a taster book for an undergraduate maths degree. Well, let me put it another way... this is a first approximation to what you might be expected to know having done a maths course, except without all those tedious proofs that take 3 years to learn. Having not done a maths degree, but occasionally wishing I had, this is a great book, allowing me to see areas of interest, with a selection of references making it easier to follow up areas where I'd like to learn more.
One of the things that worried me was that the areas I knew about seemed quite weak, and I wondered if it was weak all round, and my lack of knowledge just made the rest seem more complex. However, an investigation of Prof. Garrity's web page hints that his background is in the areas furthest from what I know, so it seems quite plausible that the book's strengths are in those areas, which are admittedly the ones I enjoyed the most.
On the downside, some of the diagrams are rather dodgy bitmaps, and the occasional typo has slipped through. Par for the course for first edition, I suppose. Still, it's all-round good mathematical entertainment for the mathematical non-mathematician.