Infinite dimensional modules for finite groups
D. J. Benson
Survey article for the Bielefeld Euroconference on infinite length modules,
Sept 1998.

\begin{abstract}
In the first lecture, I give an introduction to some of
the questions currently under investigation in the theory of finite
dimensional modular representations of finite groups.
In the second lecture, I give some idea of how the theory of infinite 
dimensional modules has recently had an impact on our understanding 
of the category of finite dimensional modules.
In the third lecture, I present recent progress on understanding phantom
maps. These may be viewed as the aspects of
infinite dimensional module theory which are invisible from the point
of view of the finite dimensional modules.
\end{abstract}