The aims of this book are various, but all stem from the author’s wish to present beautiful, interesting, living mathematics, as intuitively and informally as possible, without compromising logical rigor. Naturally, you will solidify your calculational knowledge, for this is in most applications the skill of primary importance. Second, you will acquire understanding of the theoretical underpinnings of the calculus, essentially from first principles. If you enjoy pondering the concept of infinity, this aspect of the book should appeal to you. The third major goal is to teach you something of the nature and philosophy of mathematics itself. This aspect of the presentation is intended to have general appeal, not just to students who intend to major in mathematics at the university level, but to the mathematically curious public.