(356 pages, 152 illustrations) This book is entitled "Exploratory Problems from ages 10 - 100, A Travel Guide to Mathematics." It includes 26 exploratory problems complete with questions and answers to the problems as well as a detailed explanation of the mathematics involved. In fact, 80% of each problem is devoted to a discussion of the mathematics. This feature will ensure that the teacher, even of very bright students, will have an advantage in that they will know the answers and be able to talk about them in detail. The book is an outgrowth of my 45 years of teaching. I am a Professor of Mathematics so I have taught primarily University undergraduate and graduate students, but I have also taught secondary school students, secondary teachers, and I have conducted junior high math camps in the summer-time for 25 years. Through all of this I have found that, at every level, there are students who can handle mathematical concepts far beyond what the general public would guess. This is an especially good time to introduce these problems. There is a need for students and teachers to address mathematical problems for their own sake. You can label these problems as "problems of the week," "exploratory problems," or just plain "fun problems" and you'd be surprised how many students will light up when an out-of-curriculum challenge is presented. And there are plenty of non-students who love challenges as well. Finally we should not undersell the subject of mathematics, it is a serious field of study. It assumes a natural place as a subject in elementary, middle, high school, college, and graduate school, but it is more. It is as important to the history of humanity as thought itself.