Let $x\left(n\right)$ be a bounded sequence in a Banach space X.
Rosenthal's $l^{1}$-theorem states that there is essentially only
one exceptional situation where it is $\mathit{not}$ possible to
extract a subsequence which is a weak Cauchy sequence: This happens
if (x$_{n}$) is the sequence of unit vectors in $l^{1}$.The aim
of these lectures is twofold: On the one hand results from the last
few years centering around this theorem are presented, and on the
other hand the opportunity is taken to introduce the audience to a
number of techniques which are of importance in modern Banach space
theory (Ramsey theory, Martin's axiom, ... ).
