This book is dedicated to compressible aerodynamic flows in the context of the inviscid fluid hypothesis. Each chapter offers a simple theoretical presentation followed by an overview of practical calculation methods based on recent results, in order to make theoretical understanding easier and present current applications. Chapters 1 through 8 introduce the fundamental principles of theoretical aerodynamics and continue with vital reminders for understanding the discussions in the following chapters. Chapters 9 through 17 present the theory of steady unidimensional flows and breach surfaces such as shock waves and flow lines. This is central to gas dynamics. Chapters 18 through 24 develop the theory of characteristics applied to the study of supersonic flows as well as unsteady flows. The final chapter describes specific properties of transonic flows.