Quantitative finance, also known as mathematical finance, is a field of applied mathematics, concerned with financial markets. Generally, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. In particular mathematical finance has been ranked, without a doubt, as the first among many and quants, as mathematicians are known in the industry, have been blamed for developing and using esoteric models which are believed to have caused the deepening of the financial crisis. As in many fields of science, mathematics plays a relevant role in finance. The basis of financial theory is an analysis of actions of ‘economic agents’ on an effective use of resources under uncertainty, and as a complex procedure, it makes necessary the use of advanced methods of mathematical modeling, the application of which has a direct and considerable impact on the financial world. This Book ‘Quantitative Finance’ presents perspective on how the development of finance theory has influenced and in turn been influenced by the development of mathematical finance theory. It evaluates the importance of using mathematical modeling tools in finance and discussion of its positive and negative influence on financial markets. The use of such methods in finance might take different directions regarding various aspects of financial market types, each of which might involve sophisticated analytical and numerical techniques. Therefore, with enormous fluctuations occurring frequently in the financial markets the demand for better forecasting and decision-making methods is increasing. Since organizations responsible for producing economic and financial forecasts have a huge amount of information to process and a growing variety of techniques. So, financial practitioners must not only heavily rely on them, but on their intuition and judgment. Only the proper use of mathematical models in finance with consideration of all accurate financial data, trends of financial markets, and useful variables of a system might bring a good understanding of dynamic markets and assist practitioners to make financial projections and decisions adequately.