This textbook is intended as a guide for a two- or three-semester calculus course and is aimed at students of mathematics and physics, as well as mathematically inclined students of computer science and the exact sciences. Detailed proofs and explanations, along with numerous examples and interesting exercises, make it very suitable for mathematical self-study. A clear and organized structure, along with a clever arrangement of the material, allows the focus to be placed on core areas during the initial study. Instructors are provided with various options to emphasize different topics depending on the nature of the lecture and to choose suitable methods for presenting the material. Geometric intuition and historical motivation, combined with a moderate level of abstraction, characterize this modern introduction to calculus.