The possibility of accessing and processing huge quantities of data on financial markets opens the path to new methodologies where systematic comparison between theories and real data not only becomes possible, but mandatory. This book summarizes recent theoretical developments inspired by statistical physics in the description of the potential moves in financial markets, and its application to derivative pricing and risk control. It takes a physicist's point of view to financial risk by comparing theory with experiment. Starting with important results in probability theory, the authors discuss the statistical analysis of real data, the empirical determination of statistical laws, the definition of risk, the theory of optimal portfolio, and the problem of derivatives (forward contracts, options). This book will be of interest to physicists interested in finance, quantitative analysts in financial institutions, risk managers and graduate students in mathematical finance.