At first when I began to read from this book it felt an easy, simple to read book giving clarity rather than anchoring you down with complicated notation and language. However, the simplicity is at a payoff, later topics within chapter 7 and onwards lack enough rigour to really give you the ability to be able to use it in application (although the concepts remains clear). The book is riddled with 'typos'/'mistakes'; within proofs and exercise and derivations of formulas, so you lose time trying to understand or solve questions which will inherently lead you to the wrong conclusions relative to what the question is implying to. So it has naturally lead to frustration and doubt whether the question are worth the effort. The 'loose' definitions restrict logical growth and certain concepts are to brief to give the full weight of their importance.
They have given you the map but not the compass and a legend for the map. So while you may understand the concepts, it's beauty is left hidden in the exercises! I felt slightly robbed that they may of been a bit lazy in leaving all the work in the exercises. As a mathematician I understand the necessity of exercises but only if they lead or provide you the tools to be able to complete them; this is where I feel they went wrong (mistakes included).
Finally, the examples are basic and do not fully explore the definitions or theorems.
It is a good book for the very, very basics and if you don't read too deeply into it; so overall, disappointed, expected more from a Ian Stewart book. For a fuller grasp of the subject you will need another book; you have been warned.