The author of an easily read study of a very difficult subject has provided a series of essays on different areas of higher mathematics. Beginning with a discussion of arithmetic and the theory of numbers, she continues through the concept of the infinite and the transfinite. Geometry from Euclid to the modern theories are briefly reviewed and there is a discussion of analytic geometry and its importance, the general concepts of multi-dimensional space, the ideas underlying the science of topology. The chapter of calculus is particularly well done. In presenting many of these subjects, the author indicates not only what theory the mathematician has developed but provides some understanding of his reasoning and methods. The reader who wishes to obtain a general knowledge of higher mathematics will find this a thoroughly satisfactory introduction.