Commutative algebra and duality in the cohomology of groups
Dave Benson

Lecture notes for four lectures given at the ICTP, Trieste, 2004. 

\begin{abstract}
I shall use duality in the cohomology rings of finite groups as a motivation
for a discussion of what the word ``Gorenstein'' should really
mean in a more general context than usual.
\end{abstract}

Lecture 1: What is group cohomology?
Lecture 2: Local cohomology of group cohomology.
Lecture 3: What is Gorenstein, really?
Lecture 4: Duality in algebra and topology.