This book is full of very lively and engaging explanations of a wide range of mathematics. The book consists of four parts, each of which is subdivided into three chapters. The first part is on "Understanding Uncertainty" and covers topics related to chaos, coincidences, and statistics. The second part, "Embracing Figures", deals with cryptography and patterns and has an especially nice section on `sizing up numbers' which deals with orders of magnitude and topics which should be a part of anybody's quantitative literacy. "Exploring Aesthetics" is the subject of the third part, which includes discussions of fractals and chaos and a nice introduction to the coffee cups and doughnuts of topology. They also discuss Mobius Bands and Klein Bottles, which lead nicely into the final section, which is entitled "Transcending Reality", and deals with the fourth dimension and various notions of infinity.
That is a large number of topics to cover in 288 pages, and doing a little division will tell you that many topics are treated extremely briefly. And that would probably be many readers' main criticism of the book: while it certainly gives a sampling platter of a large number of ideas throughout mathematics, it does not give you an entire meal of any of them, and before you are even done chewing one bite, the authors bring you the next topic served on a platter. While I certainly understand, and to some extent agree with, this criticism, I think that many readers will prefer their mathematics served this way, and it certainly will open the door for many of them to explore these ideas further.
Burger and Starbird take the subtitle of their book - "Making Light Out Of Weighty Matters" - quite seriously, and their exposition is filled with jokes and asides ranging from the corny to the extremely corny. I found the writing style to be fun, and I think that it would help bring in many readers who would be turned off by a more serious approach to exposition.
On the whole I think the authors succeed in their goal remarkably well: readers with little or no mathematical background will walk away from the book having learned a little bit about a lot of different mathematical topics. Hopefully, they also will have their appetites whetted for further - and deeper - learning and they will find some of the other popular math books populating their bookstore's shelves to satisfy this hunger. Most importantly, any reader of Burger and Starbird's book will realize that mathematics is a far more creative and exciting field than they may have gathered from their prior courses and experiences.