The book develops concepts and a methodology for a rational description of the organization of three-dimensional flows considering especially the case where the flow is the detachment place. The descriptive analysis based on the singular points theory of Poincaré develops conventional but rather unfamiliar considerations from aerodynamicists, who face the understanding of complex flows including separation lines and many vortices. These problems concern the industrial sectors where aerodynamics plays a key role: aerospace, ground vehicles, buildings, etc.