We propose an fresh look on the ideas of Andre Weil, who has spent about 2 years at this university. In his book "L'integration dans les groupes topologiques et ses applications" he has lead the foundations of what many people have called abstract harmonic analysis (over locally compact Abelian groups). While it was certainly Weil's idea to provide a unified approach to quite differently looking situations (the torus, integers, Eucledian spaces, p-adic groups) the ``abstract'' setting began to loose contact with the ``concrete/applied'' settings which are of high relevance for a number of applications, e.g. in signal and image processing, or for mobile communication.

The developments in modern time-frequency analysis, in particular the foundations of Gabor Analysis make clear that the CONCEPTS proposed by A.Weil are extremely helpful in order to describe the basic ideas in a mathematically well founded manner. Moreover, they even lend themselves to a theoretical description as well as an approximate numerical realization on a computer. In this way the ``abstract concepts'' become a guideline for these application areas, and are now only abstract in the sense of a concentration on the essential features, but not in the spirit of being impractical or far away from applications.