  Thye theory of frames for a Hilbert space plays a fundamental role in signal
processing, image processing, data compression, sampling theory and much more,
as well as being a fruitful area of research in abstract mathematics. In this
``tutorial'' on abstract frame theory, we will try to point out the major
directions of research in abstract frame theory and give some sample techniques
from each of the areas. We will also bring out some of the important open
questions, discuss some of the limitations of the existing theory, and point to
some new directions for research.
