Calculus I: A Complete Course in Single-Variable Calculus provides a rigorous, readable path from the real number system through limits, continuity, differentiation, integration, applications, sequences, and infinite series. Written for students entering degree-level mathematics, physics, engineering, quantitative biology, or actuarial science, the book develops formal definitions and complete proofs while maintaining a clear connection between theory and computation. Major theorems are proved in full, epsilon-delta and epsilon-N methods are developed systematically, and each chapter includes exercises with detailed step-by-step solutions. This comprehensive college-level text supports both an honours calculus course and independent study, building the conceptual depth needed for further work in mathematical analysis and the sciences.