I used this text for a course I taught as it was the default textbook at my university. The order of the material was not to my taste: for example quantifiers (second order logic) are introduced before negation etc. (first order logic), which only serves to muddle the logic. In general, concepts are treated in a somewhat informal way and I do not feel the students were able to grasp the structure of a proof from this approach.The text is littered with "Historical Comments" and "Mathematical Perspectives" which I found to be either insufficient (less than 1 page discussing groups in a very informal way, pg 133) or lacking in context (eg. discussion of Riemannian Geometry on pg 42).In attempt to temper the formal difficulties of proof with lively exposition the authors have produced a text which is very difficult to teach from and short-changes any independent readers.