I have just had my first look at this book. It's a slim and dense volume, packed with maths, but not quite what I was expecting. It's more about constructability and existence theorems than some of the problems that I was expecting to see (Circles of Apollonius, Simpson's Line and other geometrical problems, for example).
Instead, a typical problem is stated in algebraic form rather than geometrical (e.g. "Prove that 1/4 + 1/16 + 1/64 ... = 1/3"). A reading of the relevant chapter of What is Mathematics?: An Elementary Approach to Ideas and Methods (Oxford paperbacks)
for example would help you understand the relationship between geometrical constructions and fields, and this book would extend your knowledge if you wished.
In summary, a good book on the topic, but the topic is not necessarily what you may be expecting from the title.