The talk is going to describe the developments in Gabor Analysis in the last 25 years, when it has gained substantial momentum, both from the mathematical theory which is to some extent now well established, to the applications and numerical toolboxes.

This branch of Harmonic Analysis has enforced the development of some new concepts in functional analysis, such as Banach frames, Banach Gelfand Triples, Riesz projection bases, modulation spaces etc.., which will be explained by analogy to the corresponding concepts of Linear Algebra.

The talk should be of interest to people working in the applications, but also for mathematicians working in analysis, interested in those new methods that certainly can be applied in other branches of mathematics benefitially.