The 36th Séminaire de Probabilite's contains an advanced course on Logarithmic Sobolev Inequalities by A. Guionnet and B. Zegarlinski, as well as two shorter surveys by L. Pastur and N. O'Connell on the theory of random matrices and their links with shastic processes. The main themes of the other contributions are Logarithmic Sobolev Inequalities, Shastic Calculus, Martingale Theory and Filtrations. Besides the traditional readership of the Séminaires, this volume will be useful to researchers in statistical mechanics and mathematical finance.