In the seventies, three economists-mathematicians, Black, Scholes and Merton, discover how one can hedge and price new financial assets, called derivatives (in fact a large part of the story was present in the thesis of Bachelier (1900) but nobody took care of it). Since this time, many financial institutions need mathematicians to create and price new derivatives. My aim is to explain what are derivatives, why they are used, the main ideas behind there pricing and hedging and which mathematical tools they involve.