Can't say that the subjects are chosen very precisely either -- the Fundamental Theorem of Algebra isn't actually a theorem of algebra; Tychonoff's theorem is fundamental only to the set-theoretical part of topology; the Fundamental Theorem of Counting is just a particular case of the "Fubini" interchange-of-summations formula, which I would call the real fundamental theorem of counting. The number of platonic solids is mostly a curiosity from a modern perspective; so are the transcendences of pi and e.
Also, the word "extended" in the Number systems section needs to be taken with some artistic license; the "extension" introduces new symbols (negatives) and new relations that can occasionally render some old elements identical (in the worst case, the whole monoid can collapse to a point). The most famous example of this is what happens if you divide by 0 (= extend the multiplicative monoid of real numbers to a group). This is not something the author should be blamed for; it's the only real error I've spotted at a quick skim, and it's rare for a collection as diverse as this to have this few errors. The real problem is: what's the point of such a survey if pretty much any of the results is given so little time and space that only those who already know it can understand it from the description?