I have been using this book for a year and a half now, as support for students who need a quick reference for points of grammar they do not understand. It has been excellent in this way, and does not claim to be totally comprehensive (the blurb states 'intermediate - upper intermediate'). The test at the beginning is another way of saving time - finding the student's weakness, turning to the relevant page and fixing the problem.
True - English grammar is deceptively easy at the beginning, and becomes vast later on, but students have to start somewhere, and this book provides funny and relevant explanations. No book can claim to provide a purely systematic approach to English because the language simply has not evolved in such a way. No amount of snobbery can hide this fact. Moreover, the language is uniquely different from other European languages in that, for example, with English, there is no governmental body which has to authorize new vocabulary.
I have taught people of different nationalites, and I have noticed that speakers from Germanic linguistic groups, tend to want to apply the rigidity of their native languages to English. But English does not function in that way - and Swan has recognised this and has attempted to make the density of the language more accessable.
Grammar is explained in layman's terms and as concisely as possible - there are areas which seemingly overlap or contradict, but this is the nature of the English language itself. So there is an exactness about this book which I have witnessed tidy up points previously confusing for students. It is particularly good on the tenses for instance. It maintains a light-heartedness through its cartoons, which at the same time provide real and funny examples of grammar allowing the student to fully consolidate the target grammar point. This may just come down to your sense of humour - there are jokes about thieving bishops, 'armed' teachers, for instance, that I thought were hilarious!
So if you want an attractive alternative to the volumes of excercises allowing one to pound one's way through to an advanced level, without comprehending how to actually use English, then this is the book for you.