When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus.  In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique approach, Toeplitz summarized and elucidated the major mathematical advances that contributed to modern calculus. Reissued for the first time since 1981 and updated with a new foreword, this classic text in the field of mathematics is experiencing a resurgence of interest among students and educators of calculus today.