Computational finance deals with the mathematics of computer programs that realize financial models or systems. This book outlines the epistemic risks associated with the current valuations of different financial instruments and discusses the corresponding risk management strategies. It covers most of the research and practical areas in computational finance. Starting from traditional fundamental analysis and using algebraic and geometric tools, it is guided by the logic of science to explore information from financial data without prejudice. In fact, this book has the unique feature that it is structured around the simple requirement of objective science: the geometric structure of the data = the information contained in the data.