About the Book: This book serves as a bridge between elementary calculus and advanced analysis, emphasizing the reversible nature of differentiation and integration. It focuses on two core principles: the chain rule and its inverse, the change of variables, and the Leibniz rule (product rule) with its inverse, integration by parts. These tools are highlighted as fundamental because almost all functions can be viewed as compositions or products of simpler functions, making these techniques widely applicable. The book contains numerous worked examples and exercises, most with detailed solutions, designed to motivate readers and deepen their understanding. Its ultimate goal is to prepare students for advanced analysis and give them a broader view of useful mathematical techniques.