This book presents first year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigor for these subjects in the 19th century for one and several variables is treated in Chapters III and IV. Complemented by a large number of examples, calculations and mathematical pictures, the text offers broad motivation and profound explanations. It will provide stimulating and enjoyable reading for students as well as teachers.