Translated and adapted from a popular Russian educational series, this concise book requires only some background in high school algebra and elementary trigonometry. It explores the fundamental concept of the integral calculus: the limit of the sum of an infinitely increasing number of infinitely decreasing quantities. Mastery of this concept enables the solution of geometry and physics problems and introduces the systematic study of higher mathematics. AUTHOR: A Swiss-born Soviet mathematician, Isidor Pavlovich Natanson (1906 64) served on the faculty of Leningrad State University (now Saint Petersburg State University), specialising in real analysis and constructive function theory. Dover also published his Theory of the Functions of a Real Variable.