To begin with, after the high expectations created by the book's title and cover, the disappointment comes from what the book really contains. But let's elaborate pros first. The first two chapters are well aimed: they introduce the notion of complex systems and briefly overview the history of their research. The amount of covered material is huge which is at the same time good (most readers will find their favorite topics included) and bad (exposition is often sketchy). The list of literature is also ample and can serve as a useful signpost for newcomers.

So what's wrong with the book then? First of all, what comes after the two introductory chapters is an intellectually challenging but little organized overview of main concepts in complexity research and some results achieved in "complex" niches of other fields. Hence the use of the word explained in the title is dubious - illustrated would fit the content better. Second, despite the word complexity in the title, the book is more an overview of complex systems and the complexity itself (its various aspects and definitions) is not particularly discussed. And finally, editorial work is poor, resulting in a large number of typos, non-English sentences, and remotely related insider remarks.

Browsing Amazon results for "complex systems", the lack of a good introductory book to complex systems is apparent. Or, does anyone have a good candidate already?