The course deals with the qualitative study of oscillatory and non- oscillatory trajectories of real analytic vector fields, mainly in dimension three. In the first part of the course, we describe several kinds of asymptotic behaviour that such transcendental objects can have: axial spiraling, asymptotic linking, separation by projection. In the second part, we will study non-oscillatory trajectories that belonging to new o-minimal structures, an application of the contents of the courses given by J.-P. Rolin, R. Schäfke and F. Cano.