This extensively classroom-tested book provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. It includes clear proofs, detailed examples, and numerous exercises. The text progresses from single variable to multivariable functions, providing a logical development of material that makes the book suitable for one- and two-semester courses and prepares students for more advanced analysis-based courses. Relevant results from elementary set theory and linear algebra are summarized in the appendices.