The other reviewers who gave this book 5 stars are on the mark, and I'm frankly amazed that anyone would give it less than 5 stars.<br><br>Sure, the book may not be "perfect" according to the varying criteria and preferences of everyone on earth, but I think it comes about as close as humanly possible.  The breadth and overall quality of this book are simply astounding.  I can't remember the last time I was this excited about a book, and I totally understand another reviewer's fantasy about being stranded on an island with the book.<br><br>As far as the level of the book, there's something here for everyone genuinely interested in mathematics.  Even many high school students and general readers will find much they can understand, though I do think it would be preferable to have at least taken calculus, and maybe also some linear algebra.<br><br>General readers will find themselves drawn deeper and deeper into the book as it provides wonderful paths to discover the beauty and power of mathematics, and the experience will be far more satisfying than reading popular mathematics books which nervously avoid mathematical notation and formulas (
  
Mathematics: A Very Short Introduction







  
  
    &nbsp;and&nbsp;
  
50 Mathematical Ideas You Really Need to Know







  
  
    &nbsp;are excellent warmups for this book).  And advanced readers will also find plenty of articles pitched at a fairly high level, and will thereby be able to extend their knowledge into areas which are less familiar, thus allowing adventure beyond the confines of their specializations.<br><br>Regarding the ~$70 price, this book is an utter bargain.  Keep in mind that this is a hardback of about 1,000 pages, and its vast content compares with 10+ typical math books, so you're saving a bundle, plus you get the convenience of having all of this scope within the covers of a single carefully-integrated book.<br><br>Needless to say, this book comes with my highest possible recommendation.<br><br>Given what has been achieved with this book, now I just hope that Princeton Companions of this quality will be developed for other subject areas such as applied math, physics, chemistry, biology, philosophy, etc.