In this textbook, the author introduces the concept of unsteady aerodynamics and its underlying principles. He provides the readers with a full review of fundamental physics of the free and the forced unsteadines, the terminology and basic equations of aerodynamics ranging from incompressible flow to hypersonics. The book also covers the modern topics concerning the developments made during the last years, especially in relation to wing flappings for propulsion. The book is written for graduate and senior year undergraduate students in Aerodynamics, and it serves as a reference for experienced researchers. Each chapter includes ample examples, questions, problems and relevant references.