Though elementary in nature, this book deals with fundamental issues in mathematics — number, algebra, geometry (both Euclidean and non-Euclidean) and topology. These subjects, on an advanced level, are the same ones with which much of current mathematical research is concerned and were themselves research topics of earlier periods. The material is very suitable both for advanced high school students and for college students interested in elementary mathematics from a higher standpoint. It will also be very useful to high school teachers seeking an overview of their subject matter.