As a owner of The Princeton companion to mathematics, I have found a great deal of things to learn from it. This book covers math in almost every single field and easy to understand(after fully understand the introduction chapter and remember all those definitions.) There are history of each field, list of mathematicians and their biography, introduction to each field, what each field is concerned with. it can go deep into some topic, like what is on in the current research. but a high school student with enough mathematical skills have no problem reading it.
I suggest this book if you have math students who are really interest to mathematics and does not fear lots of definition to remember.
