  Risk control has become one of the major concern of financial institutions.
The need for adequate statistical tools to measure and anticipate the amplitude
of the potential moves of financial markets is clearly expressed, in particular
for derivative markets. Classical theories, however, are based on simplified
assumptions -- such as Gaussian statistics -- and lead to a systematic (and
sometimes dramatic) underestimation of real risks.
  We summarize a few basic notions in probability theory which are useful in a
financial context: Statistics of Extremes, Sums of Random Variables, Central
Limit Theorems and Deviations, Correlations and Dependence, and a brief
introduction to Random Matrix Theory. This self-contained text corresponds to
the first chapter of our book, `Theory of Financial Risk'.
