In its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the world and perhaps its greatest meditation on the theme of continuity.My aim throughout has been to provide a tour of the calculus, not a treatise. I have concentrated on the essentials. There are no problem sets or exercises or anything at all like that in what I have written. I have suppressed whenever possible mathematical formalism in favor of ordinary English. But there is no explaining mathematics without from time to time using mathematics, and the mathematician’s symbolism, which to an outsider looks as inviting as Chinese, does represent an instrument of matchless power and concision. It is my hope that by using this instrument sparingly the symbols might come to gleam against the background of plain prose, like jewels seen on black velvet.The argument of the book is conveyed in the text itself; down below, in the various appendices, definitions are given in their full formality and a number of theorems demonstrated. I have not proved everything that might be proved: some statements remain in the text as ringing affirmations. Nothing in the appendices is beyond the grasp of the ordinary reader, but there is no avoiding the fact that confrontation with proof is quite often a humbling experience. A feeling of helplessness steals over the soul. At first, it seems as if the confident language of mathematical assertion constitutes a subtle form of mockery. There is no help for any of this save the ancient remedies of practice and a willingness to put pencil to paper. Readers who want the big picture need not linger in the cellars; but a mathematical argument, once understood, is, in its capacity to compel belief, a miracle.