Introduction: Some Aspects of Mathematical Finance (Marc Yor). -Financial Uncertainty, Risk Measures and Strong Preferences (Hans Fِllmer). -The Notion of Arbitrage and Free Lunch in Mathematical Finance (Walter Schachermayer). -Dynamic Financial Risk Management (Pauline Barrieu and Nicole El Karoui). -Stochastic Clock and Financial Markets (Hélyette Geman). -Options and Partial Differential Equations (Damien Lamberton). -Mathematics and Finance (ةmmanuel Gobet, Gilles Pagès, Marc Yor).