Gabor Analysis can be viewed as a sub-field of time-frequency analysis,
which essentially is making use of a time-localized version of the Fourier
transform, using a certain (localization) window. D.Gabor has suggest in
1946 to use the Gauss-function, due to its optimality property for the
Heisenberg relation, and sample it over the integer lattice in TF-domain.

We will give a summary of results obtained in the last 30 years concerning
Gabor families, in particular (redundant) Gabor frames and Gabor Riesz
bases, and will try to relate these findings to applied problems, e.g. in
audio (MP3) and mobile communication, but also mention the role of
so-called Banach frames, Gelfand triples for other branches of modern
analysis.